users.polytech.unice.frusers.polytech.unice.fr/~pfz/COMPILATION/COURS/coursMALENFANT.pdf ·...

� �� ! #"%$'&(�)��+*

,.-0/�13254�6879-;:<4�=5>?-;=.@A(B<CEDGF?H<H<FJI(B;K(F?H�I(L(MONPFJB<H<MOQ<R?HS© TJU SWV?XEY[Z�\ U^] Y[_a` U _cbWdfe^g^gih

j Mlk?FJLmk?Fonqpsrtvu r nqkJMlFJLmk?F?H0FJQvnqkJMlFJLmk?F?H.K(Fxwzy MOL({PRJL(MlFJI(Bt L(MONPFJB<HWMOQ<R|K(Fx}�B<FJQ�~E{fLmF�HWImK

� ��

� ��! "� #$&%'$ j F?H)( ~+H<F?H %*%+%*%+%*%,%+%*%+%*%+%*%*%+%,%+%*%+%*%*%+%*%+%,%+%*%*%+%*%+%*%,%+%*%+%*%+%*% -$&% � . B<C/((w1032 F?H;DGC+LmKm~�2 FJL Q�~EI54 %*%+%*%*%+%,%+%*%+%*%*%+%*%+%,%+%*%*%+%*%+%*%,%+%*%+%*%+%*% 6$&%87 9 MlRJB�~EB<k;:(MlF�K(F=<>:mC/2 H@?BA %*%+%*%+%*%*%+%,%+%*%+%*%*%+%*%+%,%+%*%*%+%*%+%*%,%+%*%+%*%+%*% C

D � ��FE!��GH JIK�!�F�L��MN��GOMP�Q�R�5MP�!�NST�UI"� V�5%'$ <�C+LmHWQWBWImkJQWMlC+L K y I(L w ~EL({ ~E{PF�B<RJ{fI(wOMlFJB %,%+%*%+%*%*%+%*%+%,%+%*%*%+%*%+%*%,%+%*%+%*%+%*% W�5% � X 4qA(B<F?H�HWMlC+LmH;B<RJ{fI(wOM10JB<F?H %*%+%*%+%*%*%+%,%+%*%+%*%*%+%*%+%,%+%*%*%+%*%+%*%,%+%*%+%*%+%*%Y$PZ�5%87 [ I(Q<C/2 ~EQ<F?H)\mL(MlH %+%*%,%+%*%+%*%+%*%*%+%,%+%*%+%*%*%+%*%+%,%+%*%*%+%*%+%*%,%+%*%+%*%+%*%Y$PZ�5% ] ^ MlH<FxFJL A(B�~EQWM1_ ImF|K(F?H.~EwO{PC+BWMOQ@:�2 F?H %+%,%+%*%+%*%*%+%*%+%,%+%*%*%+%*%+%*%,%+%*%+%*%+%*%Y$`C

�5% ]�%'$ <�C+LmHWQWBWImkJQWMlC+L K(F+ab:mC/2 AmH<C+L %,%+%*%+%*%*%+%*%+%,%+%*%*%+%*%+%*%,%+%*%+%*%+%*%Y$`C�5% ]�% � <�C+LmHWQWBWImkJQWMlC+L K y I(L [ u�ced A ~EBWQWMOB0K y I(L [ uHf %,%+%*%*%+%*%+%*%,%+%*%+%*%+%*%Y$PW�5% ]�%87 <�C+LmHWQWBWImkJQWMlC+L K MOB<F?kJQ<F|K(F|wzy [ u�cgd A ~EBWQWMOB0K(Fxwzy Fh4 A(B<F?H<HWMlC+L B<RJ{fI(wOM10JB<F %+%*%+%*% � �

�5% ]�% ] ^ MOL(M'2 MlH�~EQWMlC+L K y I(L [ u�c %*%+%,%+%*%+%*%*%+%*%+%,%+%*%*%+%*%+%*%,%+%*%+%*%+%*% �&-�5%8- X 4 FJB<kJMlk?F?H %*%+%*%+%*%,%+%*%+%*%+%*%*%+%,%+%*%+%*%*%+%*%+%,%+%*%*%+%*%+%*%,%+%*%+%*%+%*% �&6

i j�kUk� JI"lm�5M`I"��onH��p�mqOkH�F�!�P�`I"��U�L�FE!��GH JIKr!�F�!� Dts75%'$ j y C+I(QWMOw�umvmw5u&x %*%+%*%,%+%*%+%*%+%*%*%+%,%+%*%+%*%*%+%*%+%,%+%*%*%+%*%+%*%,%+%*%+%*%+%*% �mC75% � [ I(QWB<F?H.k?C/2L2 ~ELmK(F?H0FJQ0C+I(QWMOwlH t L(My4 %+%,%+%*%+%*%*%+%*%+%,%+%*%*%+%*%+%*%,%+%*%+%*%+%*%g7&Z

75% �5%'$ j ~ k?C/2L2 ~ELmK(F,z�{`|B} %*%+%*%*%+%,%+%*%+%*%*%+%*%+%,%+%*%*%+%*%+%*%,%+%*%+%*%+%*%g7&Z75% �5% � j ~ k?C/2L2 ~ELmK(FL~mu&} %*%+%*%*%+%,%+%*%+%*%*%+%*%+%,%+%*%*%+%*%+%*%,%+%*%+%*%+%*%g75$75% �5%87 j y R?K MOQ<FJI(B�u��5��~ %*%+%*%+%*%*%+%,%+%*%+%*%*%+%*%+%,%+%*%*%+%*%+%*%,%+%*%+%*%+%*%g75$

75%87 j F?H0Fh4 A(B<F?H<HWMlC+LmH�B<RJ{fI(wOM10JB<F?H.K(F . FJBWw %+%,%+%*%+%*%*%+%*%+%,%+%*%*%+%*%+%*%,%+%*%+%*%+%*%g7 �

75% ] j F+2 CqK�0JwlF|C/(5�[FJQ.K(F . A Q@:mC+L FJQ�� ~?Nf~ %,%+%*%+%*%*%+%*%+%,%+%*%*%+%*%+%*%,%+%*%+%*%+%*%g7�]

� � ��Q��;l��QMP�mq�M`GU�! "�&��I"�F�!�L�mMN��G�MP��R�5MP�!�p�Rk�IJ "� i�V]�%'$ � B�~�2L2 ~EMOB<F?H0LmC+L5� k?C+L Q<Fh4qQWImFJwOwlF?H %*%*%+%,%+%*%+%*%*%+%*%+%,%+%*%*%+%*%+%*%,%+%*%+%*%+%*%g7&W]�% � [ I(Q<C/2 ~EQ<F d A(MOwlF %+%*%,%+%*%+%*%+%*%*%+%,%+%*%+%*%*%+%*%+%,%+%*%*%+%*%+%*%,%+%*%+%*%+%*%e] �

]�%87 a B�~ELmH[DGC+B@2 ~EQWMlC+LmH.K(F|{fB�~�2L2 ~EMOB<F?H %*%+%,%+%*%+%*%*%+%*%+%,%+%*%*%+%*%+%*%,%+%*%+%*%+%*%e]&]

] a [ } j X c X n ^ [ a�p � r X n

]�%875%'$ u ~+kJQ<C+BWMlH�~EQWMlC+L d { ~EImk;:mF %*%*%+%,%+%*%+%*%*%+%*%+%,%+%*%*%+%*%+%*%,%+%*%+%*%+%*%e]&]]�%875% � X wOM'2 MOL ~EQWMlC+L K(F?H�B<R?kJI(B<H<MON MOQ<R?H d { ~EImk :mF %*%+%*%+%,%+%*%*%+%*%+%*%,%+%*%+%*%+%*%e]�-

# � � "�� QV-5%'$ j ~EL({ ~E{PF d ( ~EwOMlH�F?H;H<R32 ~EL QWM1_ ImF?H %*%*%+%,%+%*%+%*%*%+%*%+%,%+%*%*%+%*%+%*%,%+%*%+%*%+%*%e]�W-5% � a AqA F?H.K(FxK(C kJI�2 FJL Q<H.FJQ c a c %*%*%+%,%+%*%+%*%*%+%*%+%,%+%*%*%+%*%+%*%,%+%*%+%*%+%*%g- �

-5%87 c a c FJQ�{fB�~�2L2 ~EMOB<F?H %+%*%+%*%+%*%*%+%,%+%*%+%*%*%+%*%+%,%+%*%*%+%*%+%*%,%+%*%+%*%+%*%g-&--5% ] j F?H0H<k;:mR32 ~+H�� ^ j %,%+%*%+%*%+%*%*%+%,%+%*%+%*%*%+%*%+%,%+%*%*%+%*%+%*%,%+%*%+%*%+%*%g-�

�,�Q�� MP�/GUl&MÌ"�� nH��N��U�� O�P�!GU��Nk ��GU�N��F��R��I"�F�!�N��Q��;l��QMP�mq�M`GU�! J "�� #�V65%'$ [ L ~Ew'A H<FxK(F?H;w ~EL({ ~E{PF?H0LmC+L5� k?C+L Q<Fh4 QWImFJwlH %+%*%+%*%*%+%*%+%,%+%*%*%+%*%+%*%,%+%*%+%*%+%*%g-&W65% � [ L ~Ew'A H<FxK(F?H<k?FJLmKm~EL Q<F %+%*%+%*%+%*%*%+%,%+%*%+%*%*%+%*%+%,%+%*%*%+%*%+%*%,%+%*%+%*%+%*%g65$

65% �5%'$ psK(R?F3{PRJLmRJB�~EwlF K(F3wzy ~EL ~Ew'AqH<F�K(F?H<k?FJLmKm~EL Q<F %+%*%+%,%+%*%*%+%*%+%*%,%+%*%+%*%+%*%g65$65% �5% � c F?H�k?FJL Q<FxB<R?kJI(B<HWMONPF %*%+%*%*%+%,%+%*%+%*%*%+%*%+%,%+%*%*%+%*%+%*%,%+%*%+%*%+%*%g6&765% �5%87 [ L ~Ew'A H<FJI(B<H�A(B<R?K MlkJQWM DGH;LmC+L5�zB<R?kJI(B<HWM DGH;K(FxQ A A F j j�� $�� %*%+%*%+%*%,%+%*%+%*%+%*% CB$

65%87 [ L ~Ew'A H<F|~+H<k?FJLmKm~EL Q<F %,%+%*%+%*%+%*%*%+%,%+%*%+%*%*%+%*%+%,%+%*%*%+%*%+%*%,%+%*%+%*%+%*% CF]65%875%'$ [ wO{PC+BWMOQ@:�2 F|K y ~EL ~Ew'A H<Fx{PRJLmRJB�~Ew %+%*%+%*%*%+%*%+%,%+%*%*%+%*%+%*%,%+%*%+%*%+%*% C/-65%875% � <�C+LmHWQWBWImkJQWMlC+L K(F?H�Q�~�((wlF?H.K y ~EL ~Ew'AqH�F|~+H<k?FJLmKm~EL Q<F K(FxQ�AqA F j r %,%+%*%+%*%+%*% C��

s j�� O�P� �PE!��QMÌ��OG��F��R��I"��L�5M MP�/I ��GUE��mMLMP��`��/�R�5MÌ"�Q�� iCB%'$ c Rh\mL(MOQWMlC+LmHvK MOBWMO{PR?F?H;A ~EB�w ~ H@A L Q�~F4 F %+%,%+%*%+%*%*%+%*%+%,%+%*%*%+%*%+%*%,%+%*%+%*%+%*%��&7CB% � nqk :mR32 ~ K(F|QWB�~+K ImkJQWMlC+L %*%+%*%+%*%*%+%,%+%*%+%*%*%+%*%+%,%+%*%*%+%*%+%*%,%+%*%+%*%+%*%��mC

CB% �5%'$ � wOM'2 MOL ~EQWMlC+L K(F?H0~+kJQWMlC+LmH0MOL Q<RJBWMlFJI(B<F?HvFJL Dz~?NPFJI(B0K y ~+kJQWMlC+LmH d w ~5B<R?K ImkJQWMlC+L %*%��&WCB% �5% � 9 RJBWMOQ�~E{PF|K(F?H.~EQWQWBWM'((I(Q<H0Km~ELmH;w ~5A(MOwlF�K y ~EL ~Ew'AqH<F %,%+%*%*%+%*%+%*%,%+%*%+%*%+%*%��&W

� �>�F��U�P� ��/�R�5MÌ"��U�LnU� nU��l�GH�R�B�QMP��e� V�i�5%'$ j Fxw ~EL({ ~E{PF�K(F3QWB�~ELmHWD C+B@2 ~EQWMlC+L��xn j %,%+%*%+%*%*%+%*%+%,%+%*%*%+%*%+%*%,%+%*%+%*%+%*%gW&7�5% � � B�~�2L2 ~EMOB<F?Hv~EQWQWBWM'((ImR?F?H.FJQ;QWB�~ELmH[DGC+B@2 ~EQWMlC+LmH %*%*%+%*%+%,%+%*%*%+%*%+%*%,%+%*%+%*%+%*%H$PZ5$�5%87 [ . p c�� ^ FJQ�w ~oQWB�~ELmH[DGC+B@2 ~EQWMlC+L K(F|K(CqkJI�2 FJL Q<H %+%*%+%,%+%*%*%+%*%+%*%,%+%*%+%*%+%*%H$PZmC

�5%875%'$ c Rh\mL(MOQWMlC+L K(Fxwzy [ . p c�� ^ %+%,%+%*%+%*%*%+%*%+%,%+%*%*%+%*%+%*%,%+%*%+%*%+%*%H$PZmC�5%875% � . ~EB<k?C+I(B<HvK(F3wzy ~EB@((B<F|K I K(CqkJI�2 FJL Q %+%*%*%+%*%+%,%+%*%*%+%*%+%*%,%+%*%+%*%+%*%H$PZ&W

� I��H JI"��F��k! UI"� �5V

� ��

� �� 0��

c ~ELmH�k?F%k;: ~EA(MOQWB<F��aLmC+ImH MOL QWB<CqK I(MlH<C+LmH)wlF?H LmC+QWMlC+LmH D C+LmKm~�2 FJL Q�~EwlF?H)K(F?H w ~EL({ ~E{PF?H DGC+B@2 FJwlH)K(FT2��32 F_ ImF3wlFxA(B<C/((w1032 F|K(F|K(Rh\mL(MOQWMlC+L FJQ;K(FxB<F?k?C+L(L ~EMlH<H�~ELmk?F|K(F?H0w ~EL({ ~E{PF?H %

�� 4�6��5-06 4�6

<�C/2L2 F�Km~ELmH;w ~ w ~EL({ ~E{PF?H0L ~EQWI(B<FJwlH � D B�~EL��c~EMlH�� ~EL({fw ~EMlH��mBWImH�H<F�� %'%'% � �(w ~ ( ~+H�F|K(FxQ<C+I(Q0w ~EL({ ~E{PF F?HWQDGC+B@2 R?F K(F?H�H<MO{fLmF?H�RJwlR32 FJL Q�~EMOB<F?H d A ~EBWQWMOB K(F?H _ ImFJwlH�H<FJB<C+L Q|DGC+B@2 R?H�wlF?H,2 C+Q<H�FJQ wlF?H|A�:(B�~+H<F?H K(F k?Fw ~EL({ ~E{PF % c ~ELmH�wlFxK(C/2 ~EMOLmF K(F?H�w ~EL({ ~E{PF?H�DGC+B@2 FJwlH��mk?F?H0HWMO{fLmF?H;RJwlR32 FJL Q�~EMOB<F?HvHcy ~EA(A FJwOwlFJL Q! �"$#&%('$)+*� &,

� �� "�.- HWMO{fLmF|RJwlR32 FJL Q�~EMOB<F � wlFJQWQWB<F�� k;:(M0/ B<F�� %'%'% �h%j y FJLmH<F32,((wlF�K(F?H H@A!2=( C+wlF?H _ I(MxA FJI(NPFJL Q1�JQWB<F I(QWMOwOMlH<R?H Km~ELmH I(L�w ~EL({ ~E{PF#K(C+L(LmR#Hcy ~EA(A FJwOwlF I(L

2$) 35426%7*98:,�� "k! �� mM1- � H<C+I(NPFJL Q;LmC+Q<R Σ

� FJLmH<F32=((wlF+\mL(M K(F|H@AB2,( C+wlF?H %j�d C$; Km~ELmH wlF?H w ~EL({ ~E{PF?H L ~EQWI(B<FJwlH0k?C+I(B�~EL Q<H�LmC+ImH A ~EBWwlC+LmH�K(F 2 C+Q<H�FJQ�K(FvA�:(B�~+H<F?H��qwlF?H�w ~EL({ ~E{PF?H

DGC+B@2 FJwlH�LmFxA ~EBWwlFJL Q _ ImFxK(F=<>42$?A@B*� &,l� U�C �U�D- H<R _ ImFJLmk?F�\mL(MlF|K(FxH A!2=( C+wlF?H.k :mC+MlHWMlH�A ~EB@2 M�I(L ~EwOA�: ~�( FJQ %

X L Q�~EL Q _ ImF�H<R _ ImFJLmk?F?H.K(F|H@AB2,( C+wlF?H��(wzy C+B<K B<F|Km~ELmH0wlF _ ImFJw ~EA(A ~EB�~EMlH<H<FJL Q0wlF?H;H@AB2,( C+wlF?H0Km~ELmH0wlF?Hk : ~FElLmF?H F?HWQ|HWMO{fL(My\ kc~EQWM D % psw K(FJNqMlFJL Q K(C+Lmk A CfH�HWM'((wlF K(FoA ~EBWwlFJB�K(FoLmC+QWMlC+LmH�K(FoA(B<Rh\�4(F C+I�K(F HWIHGL4(FA C+I(B;K(R?HWMO{fLmFJB0wlF?H�A(B<F32 MlFJB<H.FJQ�wlF?H;K(FJBWL(MlFJB<H0H A!2=( C+wlF?H.K y I(LmF|k : ~FElLmF�,

kH��EmSHqO�LnJI1GH��Ll� ��C��U�K- H<R _ ImFJLmk?F�K(F�H@A!2=( C+wlF?H�~EA(A ~EB�~EMlH<H�~EL Q�~EI K(R3((I(Q%K(F w ~3k : ~FElLmF %�FGML�qO� nJI1GH�� l U�C��N- H<R _ ImFJLmk?FxK(F�H@A!2=( C+wlF?H.~EA(A ~EB�~EMlH<H�~EL Q d w ~ \mL K(Fxw ~ok;: ~FElLmF %

j y C+B<K B<F K(F?HxH@AB2,( C+wlF?H3MOLHOmImF RJ{ ~EwlF32 FJL Q�H<I(Bvwzy C+A RJB�~EQWMlC+L�K(Fok?C+LmHWQWBWImkJQWMlC+L�K(Fok;: ~FElLmF?H d A ~EBWQWMOBK y ~EI(QWB<F?H0k;: ~FElLmF?H;A ~EBT�[I54 Q�~EA CfHWMOQWMlC+L _ ImF3wzy C+L ~EA(A FJwOwlF&<P'�@Q<P2�8SR>@B2�8UTU'�@�,

l��Ulm�5MPE!�U�5M`I"��V- LmC+Q<R?F y · yW� kfy F?HWQ�wzy C+A RJB�~EQWMlC+L A ~EB|w ~/_ ImFJwOwlF K(FJI54#k;: ~FElLmF?H H�C+L Q�k?C/2 �((MOLmR?F?H A ~EB�� I54 Q�~EA CfHWMOQWMlC+L DG~EMlH^~EL Q K y ~�( C+B<K ~EA(A ~EB�~FElQWB<F wlF?H H@AB2,( C+wlF?H K(F w ~ A(B<F32 M10JB<Fk;: ~FElLmF � Km~ELmH%wlF�2��32 F.C+B<K B<F � A(I(MlH%wlF?H�H@AB2,( C+wlF?H�K(F0w ~|H<F?k?C+LmK(Fvk : ~FElLmF � Q<C+I/�WC+I(B<H�Km~ELmHwlF*2��32 F|C+B<K B<F �h%

6 j ~EL({ ~E{PF?H;DGC+B@2 FJwlH

� qO�!�Rk� "�R��" nqC+MOB ω1 = ab FJQ ω2 = cd � ~EwlC+B<H3w ~ k?C+Lmkc~EQ<RJL ~EQWMlC+L�K(F ω1~cNPF?k ω2

� LmC+Q<R?F ω1 · ω2�

F?HWQ;RJ{ ~EwlF d abcd%

2

. ~EB3~EMOwOwlFJI(B<H��(MOw F?HWQ;H<C+I(NPFJL Q0I(QWMOwlF|K(F3A C+I(NPC+MOB0K(RJQ<FJB@2 MOLmFJB.w ~owlC+L({fImFJI(B0K y I(LmF|k;: ~FElLmF&, "�Q��QG��BG�� n I1GU�U� l� ��C��U�

ω- � LmC+Q<R?F |ω| � LmC/2,((B<F K(FoH@AB2,( C+wlF?H|~EA(A ~EB�~EMlH<H�~EL Q|Km~ELmHw ~ k : ~FElLmF %

<�C/2 A(Q<F|Q<FJL I K(F3w ~oA(B<C+A(BWMlRJQ<R|K(FxwlC+L({fImFJI(B�� MOw Fh4qMlHWQ<F3I(LmF�k : ~FElLmF*_ I(M H<FxK MlHWQWMOL({fImF K(F3Q<C+I(Q<FxwlF?H~EI(QWB<F?H;A ~EB�wlFxDG~EMOQ)_ I y FJwOwlF�~5wlC+L({fImFJI(B Z � w ~ <>42$?A@B*��T��6*�,

l� U�C �U��I"nH��- LmC+Q<R?F ε �)kfy F?HWQ5w ~ k;: ~FElLmF k?C+L Q<FJL ~EL Q ~EImkJI(L'H@AB2,( C+wlF�� K(F wlC+L({fImFJI(B Z� kfy F?H<Q � d � K MOB<F |ε| = 0�h%

j ~ LmC+QWMlC+L K(F w ~EL({ ~E{PF DGC+B@2 FJw.F?HWQ FJL B<Rc~EwOMOQ<R Fh4qQWBP�32 F32 FJL Q H<M'2 A(wlFD,�I(L )W2$@ 2�6* �9'��#&*>)3F?HWQHWM'2 A(wlF32 FJL Q0I(L FJLmH<F32=((wlF|K(F|k;: ~FElLmF?H0K(Rh\mL(MlF?H0H<I(B�I(L k?FJBWQ�~EMOL ~EwOA�: ~�( FJQ�,

"��U�� /�R�! �- FJLmH<F32,((wlF K(F|k : ~FElLmF?H.K(Rh\mL(MlF?H0HWI(B�I(L k?FJBWQ�~EMOL ~EwOA�: ~�( FJQ Σ%

� qO�!�Rk� "�R��1D nqC+MOQ3I(L�~EwOA�: ~�( FJQ Σ = {0, 1} � C+L A FJI(QxK(Rh\mL(MOBxwlF w ~EL({ ~E{PF j K(F?HxH<R _ ImFJLmk?F?HxK(F ZFJQ $ DGC+B@2 ~EL Q5K(F?H|A ~EwOMOLmK B��/2 F?H��kfy F?HWQ � d � K MOB<Fp_ ImFowzy C+L�A FJI(QxwlF?H|wOMOB<F MOLmK M0/ RJB<F32L2 FJL QoK(F { ~EImk;:mF dK B<C+MOQ<F|C+I K(FxK B<C+MOQ<F d { ~EImk :mF %

2

j ~oB<FJw ~EQWMlC+L FJL QWB<F5~EwOA�: ~�( FJQ0FJQ;w ~EL({ ~E{PF F?HWQ0k?C+LmHWI�(mH<Q�~EL QWMlFJwOwlF ,mH�~ELmH0~EwOA�: ~�( FJQ��mA ~+H.K(Fxw ~EL({ ~E{PF %� A ~EBWQWMOB�K y I(L ~EwOA�: ~�( FJQ%K(C+L(LmR��PQ<C+I(Q�FJLmH<F32,((wlF;K(F�k;: ~FElLmF?H�DGC+B@2 R�HWI(B�k?FJQ%~EwOA�: ~�( FJQ�F?HWQ�I(L w ~EL({ ~E{PF %j ~ LmC+QWMlC+L K y MOLmkJwOImHWMlC+L FJLmH<F32=((wOMlHWQ<FvLmC+ImH A FJB@2 FJQ K(F3k?C/2 A ~EB<FJB�wlF?H�w ~EL({ ~E{PF?H ,qC+L A FJI(Q�A ~EBWwlFJB�K y I(Lw ~EL({ ~E{PF L1

_ I(M H<FJB�~EMOQ�MOLmkJwOImH Km~ELmH�I(L w ~EL({ ~E{PF L2� kfy F?HWQ � d � K MOB<F�_ ImF;Q<C+I(Q<F?H�wlF?H k : ~FElLmF?H�K I w ~EL({ ~E{PF

L1~EA(A ~EB�~EMlH<H<FJL Q�Km~ELmH wlF%w ~EL({ ~E{PF L2

%�. ~EB@2 M(Q<C+ImH wlF?H)w ~EL({ ~E{PF?H _ ImF%wzy C+L A FJI(Q DGC+B@2 FJB�FJL k?C/2,((MOL ~EL QZ � $ C+I A(wOImHWMlFJI(B<H3H@AB2,( C+wlF?HvK y I(L k?FJBWQ�~EMOL#~EwOA�: ~�( FJQ�� MOw�FJL F?HWQ0I(L A ~EBWQWMlkJI(wOMlFJBvKm~ELmHvwlF _ ImFJw Q<C+ImH.wlF?H~EI(QWB<F?H;w ~EL({ ~E{PF?H.H<C+L Q0MOLmkJwOImH:,(wlF )W2$@ 2� * 8 '�8 2$) ,

Σ∗ - FJLmH<F32,((wlF�K(F�Q<C+I(Q<F?H wlF?H)k : ~FElLmF?H�_ ImF�wzy C+L5A FJI(Q D C+B@2 FJB HWI(B wzy ~EwOA�: ~�( FJQ Σ �PA|k?C/2 A(BWMlHw ~ k : ~FElLmFxNqMlK(F ε%

� L A FJI(QvLmC+Q<FJB�_ ImF5wlF�w ~EL({ ~E{PF Σ∗ F?HWQ.D C+B@2 R5K(F5w ~ k?C/2=((MOL ~EQ<C+MOB<F FJL A CfH<MOQWMlC+L FJQxFJL wlC+L({fImFJI(BK(F;Q<C+ImH%wlF?H%H@AB2,( C+wlF?H%K(F0wzy ~EwOA�: ~�( FJQ Σ �PFJQ�K(C+Lmk _ ImF;Q<C+I(Q%w ~EL({ ~E{PF�DGC+B@2 R0H<I(B Σ F?HWQ%LmR?k?F?H<H�~EMOB<F32 FJL QI(L H<C+ImH � FJLmH<F32=((wlFvK(F Σ∗ % <vy F?HWQ A C+I(B k?FJQWQ<F0B�~EMlH�C+L _ ImF;wzy C+L ~EA(A FJwOwlF Σ∗ wlF�)02$@� 2�6*!8 '�8 2$) HWI(B Σ

% j Fw ~EL({ ~E{PFvk?C/2 A(wlFJQ�k?C+L QWMlFJL Qb((MlFJL H��(B�I(L LmC/2=((B<F0MOL5\mL(M K(F0k;: ~FElLmF?H�� A(I(MlH;_ ImF0wlF?H�k;: ~FElLmF?H�LmF.H<C+L Q�A ~+H( C+BWLmR?F?H�FJL wlC+L({fImFJI(B %�. C+I(BWQ�~EL Q��mMOw F?HWQ;~+H<H<F��vDz~+kJMOwlFxK y RJL I�2 RJB<FJB0k?F3w ~EL({ ~E{PF , C+L k?C/2L2 FJLmk?FxA ~EB�w ~k : ~FElLmF3NqMlK(F��qA(I(MlH wlF?H�k : ~FElLmF?H;K(FvwlC+L({fImFJI(B;k?C+L Q<Fc~EL Q0k;: ~+kJI(L K(F?H�H@AB2,( C+wlF?H�K(F3wzy ~EwOA�: ~�( FJQ�� A(I(MlH�C+LA ~+H<H<F|~EI54 k : ~FElLmF?HvK(F3wlC+L({fImFJI(B � �(FJQ<k %

X LoA(wOImH)K I5w ~EL({ ~E{PF k?C/2 A(wlFJQ��+C+L5A FJI(Q K(Rh\mL(MOB K y ~EI(QWB<F?H)w ~EL({ ~E{PF?H A ~EBWQWMlkJI(wOMlFJB<H�k?C/2L2 F�wlF�w ~EL({ ~E{PFNqMlK(F.HWI(B Σ � L = ∅ _ I(M LmFvk?C+L QWMlFJL Qv~EImkJI(LmFvk;: ~FElLmF % p w LmF0DG~EI(Q�A ~+H�k?C+L D C+LmK B<FvwlF.w ~EL({ ~E{PFvN MlK(Fx~?NPF?kwlF w ~EL({ ~E{PF�_ I(M(LmF�k?C+L QWMlFJL Q _ ImF w ~3k : ~FElLmF0N MlK(F�� {ε} �m_ I(M(wOI(M(L y F?H<Q�A ~+H�NqMlK(Fb2 ~EMlH�k?C+L QWMlFJL Q�I(LmF;H�FJI(wlFk : ~FElLmF�� w ~ok : ~FElLmF�N MlK(F %

�� 5:� "!�4�6 > � = #5-$!�4�=.@ -;2�%

c FJI54 A(B<C/((w1032 F?H%D C+LmKm~�2 FJL Q�~EI54 H<F A CfH<FJL Q�Km~ELmH�wlF;K(C/2 ~EMOLmF.K(F?H�w ~EL({ ~E{PF?H%D C+B@2 FJwlH��PFJQ%k?F?H%K(FJI54A(B<C/((w1032 F?H0H�C+L Q0FJL B<Rc~EwOMOQ<R|MOL QWM'2 F32 FJL QvwOMlR?H:,

$&%87L9 MlRJB�~EB<k :(MlF K(F,<>:mC/2 H@?!A C

$&% <�C/2L2 FJL QvK(Rh\mL(MOB0I(L w ~EL({ ~E{PF�FJL MOL Q<FJLmH<MlC+L��5%�� Q�~EL Q K(C+L(LmR�I(L|w ~EL({ ~E{PF L HWI(B Σ �?k?C/2L2 FJL Q)K(R?kJMlK(FJB � 2 R?kc~EL(M1_ ImF32 FJL Q � HWM I(LmF�k : ~FElLmF ω ∈ Σ∗

~EA(A ~EBWQWMlFJL Q d L C+I LmC+L��X L F>/ FJQ�� wlF?H�w ~EL({ ~E{PF?H�H<C+L Q�K(F?H FJLmH<F32,((wlF?H % j ~=2 ~EL(M10JB<F.w ~�A(wOImH�HWM'2 A(wlFvK(F3K(Rh\mL(MOB�I(L FJLmH<F32=((wlF

F?HWQ%FJL Fh4qQ<FJLmH<MlC+L ,fMOw H<IHG Q�K(F;wOMlH<Q<FJB�Q<C+I(Q<F?H%wlF?H�k : ~FElLmF?H�~EA(A ~EBWQ<FJL ~EL Q d k?F0w ~EL({ ~E{PF % <�FJQWQ<Fv~EA(A(B<C k;:mFL y F?HWQ ((MlFJL#FJL Q<FJLmK I#A CfH<HWM'((wlF,_ ImFoHWM wlF w ~EL({ ~E{PF F?HWQ�� @�TU� kfy F?HWQ � d � K MOB<FoHcy MOw k?C+L QWMlFJL QxI(L LmC/2,((B<F=\mL(MK(F0k;: ~FElLmF?H % j F?H�k;: ~FElLmF?H�k?C+LmH<QWBWImkJQWM'((wlF?H�L y RJQ�~EL Q�A ~+H ( C+BWLmR?F?H�FJL wlC+L({fImFJI(B��qC+L A FJI(Q�k?C+LmHWQWBWI(MOB<F0I(LmFMOL5\mL(MOQ<R�K(Fxk;: ~FElLmF�HWI(B0I(L ~EwOA�: ~�( FJQ�� wlF?H�w ~EL({ ~E{PF?H;MOL Q<RJB<F?H<H�~EL Q<Hvk?C+L QWMlFJL(LmFJL QvK(C+Lmk�wlF3A(wOImH0H<C+I(NPFJL QI(L LmC/2=((B<FxMOL5\mL(M�K(Fxk;: ~FElLmF?H %n M�I(L#w ~EL({ ~E{PF k?C+L QWMlFJL Q5I(L�LmC/2,((B<F MOL5\mL(M%K(F k : ~FElLmF?H�� MOw%K(FJNqMlFJL Q|M'2 A CfH<HWM'((wlF K(F wlF K(Rh\mL(MOB FJL

Fh4 Q<FJLmHWMlC+L % psw�Dz~EI(Q K(C+Lmk A ~+H<H<FJB d I(LmF K(Rh\mL(MOQWMlC+L'FJL�MOL Q<FJLmHWMlC+L % j y Fh4 F32 A(wlF K(F?H A ~EwOMOLmK B��/2 F?H HWI(BΣ = {0, 1} DG~EMOQ|~EA(A FJw d I(LmF K(Rh\mL(MOQWMlC+L�FJL MOL Q<FJLmHWMlC+LM�O((MlFJL _ ImF5k?FJwOwlF _ ImF5LmC+ImH|~?NPC+LmHxK(C+L(LmR?FoLmFH<C+MOQ�A ~+H0QWB 0?H D C+B@2 FJwOwlF %�X L Dz~EMOQ�� w ~oA(B<C+A(BWMlRJQ<R�K(FxH�FxwOMOB<F3MOLmK M0/ RJB<F32L2 FJL QvK(F|{ ~EImk :mF d K B<C+MOQ<F|C+I K(FK B<C+MOQ<F d { ~EImk :mF3K(C+L(LmF.I(L kJBWMOQ 0JB<F.A FJB@2 FJQWQ�~EL Q�K(F0K(R?kJMlK(FJB�HWM I(LmF0k : ~FElLmF3K(F Σ∗ ~EA(A ~EBWQWMlFJL Q C+I LmC+L~EI w ~EL({ ~E{PF|K(F?H;A ~EwOMOLmK B��/2 F?H.HWI(B Σ

%f C+ImH3NPC+MlkJM%K(C+Lmk K(R � d HWI(B3wlF?HxA(w ~EQ<F?H � ( ~ELmK(F?H�K I�H<F?k?C+LmK A(B<C/((w1032 F1, k?C/2L2 FJL Q K(R?kJMlK(FJB�HWM I(LmF

k : ~FElLmF ~EA(A ~EBWQWMlFJL Q�~EI w ~EL({ ~E{PF %�[ NPF?k w ~ K(Rh\mL(MOQWMlC+L A(B<R?k?R?K(FJL Q<F�� NPC+ImH3A C+I(NPF��5Q<C+ImH3K(R?kJMlK(FJBxHWM)I(LmFk : ~FElLmF5~EA(A ~EBWQWMlFJL Q3~EI w ~EL({ ~E{PF|K(F?H�A ~EwOMOLmK B��/2 F?HvC+I LmC+LD,� 01010 F?HWQ�I(L A ~EwOMOLmK B��/2 F�� ~EwlC+B<H _ ImF� 01100 L y FJL F?HWQ�A ~+H�I(L %<�FJBWQ<F?H3w ~ Dz~+kJI(wOQ<RoK(F5wzy : I�2 ~EMOL�K y MOL Q<FJBWA(B<RJQ<FJB wlF?H3K(Rh\mL(MOQWMlC+LmH|FJL w ~EL({ ~E{PF L ~EQWI(B<FJw�A C+I(BxK(R?kJMlK(FJB

F?HWQ5QWB 0?H�A(I(MlH�H�~EL Q<F % <�F�_ I(M�MOL Q<RJB<F?H<H�F wzy MOL DGC+B@2 ~EQWMlkJMlFJLM� kfy F?HWQ5A(wOI(Q��+QoK(F H�~cNPC+MOB5Hcy MOw�A FJI(Q5R?kJBWMOB<F I(LA(B<C+{fB�~�2L2 F�_ I(M A(I(MlH<H<F�wOMOB<F.I(LmF0k;: ~FElLmF3FJQ�K(R?kJMlK(FJB HWM k?FJQWQ<F.k : ~FElLmFx~EA(A ~EBWQWMlFJL Q�C+I LmC+L d I(L k?FJBWQ�~EMOLw ~EL({ ~E{PF % <�F|A(B<C/((w1032 F�F?HWQ0~EL ~EwlC+{fImF d k?FJwOI(M�K(FxK(R?kJMlK(FJB.H<M I(LmFxA�:(B�~+H<F|FJL D B�~EL��c~EMlH0F?H<Q�{fB�~�2L2 ~EQWMy�kc~EwlF32 FJL Q FJQ|C+BWQ@:mC+{fB�~EA�:(M1_ ImF32 FJL Q5k?C+BWB<F?kJQ<F % psw�F?HWQ|~EImH<HWM%~EL ~EwlC+{fImF�� k?C/2L2 FoLmC+ImH|wlFoNPFJBWB<C+LmHxA(wOImHwlC+MOLM� d k?FJwOI(M�K(F|K(R?kJMlK(FJBvHWM I(L A(B<C+{fB�~�2L2 F5R?kJBWMOQ.Km~ELmH0I(L k?FJBWQ�~EMOL w ~EL({ ~E{PF K(FxA(B<C+{fB�~�2L2 ~EQWMlC+L#F?HWQH@AqL Q�~F4 M1_ ImF32 FJL Q.k?C+BWB<F?kJQ0C+I LmC+L %t LmF;DG~$�?C+L K(F0B<R?H�C+ImK B<F0wlF.H<F?k?C+LmK A(B<C/((w1032 F3k?C+LmHWMlH<Q<F.K(C+Lmk d k?C+LmHWQWBWI(MOB<Fvk?F _ ImF0wzy C+L Nf~�~EA(A FJwlFJB

I(L 2 <P<�*S3B8S*��A C+I(B I(L w ~EL({ ~E{PF L , I(LmF A(B<Cqk?R?K I(B<F 2 R?kc~EL(M1_ ImF _ I(M � wlC+B<H;_ I y C+L wOI(M;H�C+I�2 FJQ I(LmFk : ~FElLmF ω � B<RJA C+LmK NqB�~EM HWM ω ∈ L FJQ DG~EI54 HWMOLmC+L %

Accepteur010010

vrai

faux

�� - � /�� 4 # 4�� !�6��

<�C/2L2 FJL Q3k?C+LmHWQWBWI(MOB<F�k?FJQ.~+k?k?FJA(Q<FJI(B�� [ ImH<HWM H<I(BWA(B<FJL ~EL Q�_ ImFxk?FJw ~ A(I(MlH<H<F3A ~EB�~FElQWB<F�� w ~ kc~EA ~+kJMOQ<Rd k?C+LmHWQWBWI(MOB<FoI(L#Q<FJw%~+k?k?FJA(Q<FJI(B�K(RJA FJLmK#K(Fow ~ k?C/2 A(wlFh4 MOQ<R K(F5w ~ HWQWBWImkJQWI(B<F K(F?Hxk : ~FElLmF?H K(F L FJQxMOwFh4 MlHWQ<F3FJL Dz~EMOQ�K(F?H w ~EL({ ~E{PF?H A C+I(B wlF?H _ ImFJwlH LmC+ImH LmF3H�~?NPC+LmH A ~+H�k?C+LmH<QWBWI(MOB<FxK y ~+k?k?FJA(Q<FJI(B<H %�^ MlFJI54 �qMOwF?HWQ MOL Q<RJB<F?H�H�~EL Q0K(Fxkc~EB�~+kJQ<RJBWMlH�FJB�wlF?H w ~EL({ ~E{PF?H;FJL D C+LmkJQWMlC+L K(Fvw ~��EK M0G kJI(wOQ<R�� K(F3H�~ B<F?k?C+L(L ~EMlH<H^~ELmk?F��K M0G kJI(wOQ<Rp_ I(M�H<FoB<F>O�0JQ<F Km~ELmH|w ~ _ I ~EL QWMOQ<R K(F B<F?H<H�C+I(B<k?F?H � 2 R32 C+MOB<F�� Q<F32 AmH�� %'%'% � LmR?k?F?H<H�~EMOB<F?H|A C+I(Bk?FJQWQ<FxB<F?k?C+L(L ~EMlH<H^~ELmk?F %

<�FJBWQ�~EMOLmH w ~EL({ ~E{PF?H H<C+L Q QWB 0?H DG~+kJMOwlF?H d B<F?k?C+L(L ~FElQWB<F % j F w ~EL({ ~E{PF N MlK(F��C+I wlF w ~EL({ ~E{PF _ I(M0LmFk?C+L QWMlFJL Q>_ ImF�w ~.k;: ~FElLmF�NqMlK(F�H<C+L Q�QWB 0?H)Dz~+kJMOwlF d B<F?k?C+L(L ~FElQWB<F % j F�w ~EL({ ~E{PF;k?C/2 A(wlFJQ Σ∗ ��((MlFJLN_ I y MOL5\mL(M �

� j ~EL({ ~E{PF?H;DGC+B@2 FJwlH

F?HWQ�~EImH<HWMqQWB 0?H)Dz~+kJMOwlF d B<F?k?C+L(L ~FElQWB<F��fA(I(MlH;_ I y d A ~EBWQWMOB�K I 2 C/2 FJL Q%C$;oI(LmF k : ~FElLmF;LmF�k?C+L QWMlFJL Q _ ImF K(F?HH@AB2,( C+wlF?H K(F0wzy ~EwOA�: ~�( FJQ Σ � FJwOwlF3~EA(A ~EBWQWMlFJL Q d Σ∗

% }�MlFJL H��(B�� Q<C+ImH�wlF?H�w ~EL({ ~E{PF?H \mL(MlH kfy F?HWQ � d � K MOB<F3LmFk?C+L Q<FJL ~EL Q _ I y I(L LmC/2=((B<Fb\mL(M K(F;k;: ~FElLmF?H��PH<C+L Q�DG~+kJMOwlF?H d B<F?k?C+L(L ~FElQWB<F;A(I(MlH _ I y MOw HWIHG Q�K(F)2 R32 C+BWMlH<FJB� Km~ELmH;I(L _ I ~EL QWMOQ<R*\mL(MlF|K(F�2 R32 C+MOB<F � Q<C+I(Q<F?H0wlF?H;k : ~FElLmF?Hv~+k?k?FJA(Q�~�((wlF?H %<�FxH<C+L Q;K(C+Lmk3wlF?H�w ~EL({ ~E{PF?H;MOL5\mL(MlH)_ I(M A CfH<FJL Q�A(B<C/((w1032 F %�X L B<Rc~EwOMOQ<R��(w ~ Dz~+kJMOwOMOQ<RxC+I w ~5K M0G kJI(wOQ<R

K(F�w ~vB<F?k?C+L(L ~EMlH<H�~ELmk?F;K(RJA FJLmKoK(F w ~vHWQWBWImkJQWI(B<F;K(F?H�k : ~FElLmF?H�~+K52 MlH<HWM'((wlF?H % j F?H�~+k?k?FJA(Q<FJI(B<H�K(F k?FJBWQ�~EMOLmHw ~EL({ ~E{PF?H3LmF5LmR?k?F?H<HWMOQ<FJL QvA ~EBxFh4(F32 A(wlF _ I y I(LmF _ I ~EL QWMOQ<R \mL(MlFoK(F,2 R32 C+MOB<F��t2��32 FoHWM k?F?Hvw ~EL({ ~E{PF?HH<C+L Q MOL5\mL(MlH % c y ~EI(QWB<F?H LmR?k?F?H<HWMOQ<FJL Q I(LmF 2 R32 C+MOB<F LmC+L5� ( C+BWLmR?F {PRJB<R?F k?C/2L2 F I(LmF A(MOwlF % c y ~EI(QWB<F?HFJLmk?C+B<FxLmR?k?F?H<H<MOQ<FJL Q0I(LmF*2 R32 C+MOB<FxLmC+L5� ( C+BWLmR?F d ~+k?k 0?H.~EwlRc~EQ<C+MOB<F � �� h%

f CP~�2 <>:mC/2 H@?BA5~.A(B<C+A CfH<R I(LmF :(MlRJB�~EB<k :(MlF.K(F?H w ~EL({ ~E{PF?H�FJLoD C+LmkJQWMlC+L K(F�w ~vA(wOImH A FJQWMOQ<F _ I ~EL QWMOQ<RK(FxB<F?H<H�C+I(B<k?F?H�LmR?k?F?H<H�~EMOB<F?H d wlFJI(B<H0~+k?k?FJA(Q<FJI(B<H %�� I ~EQWB<F|{fB�~ELmK(F?H0kc~EQ<RJ{PC+BWMlF?HvH<C+L Q;K(Rh\mL(MlF?H�,$&% wlF?H;w ~EL({ ~E{PF?H;B�~EQWMlC+L(LmFJwlHvC+I B<RJ{fI(wOMlFJB<H��

�5% wlF?H;w ~EL({ ~E{PF?H;MOLmK(RJA FJLmKm~EL Q<HvK I k?C+L Q<Fh4 Q<F��75% wlF?H;w ~EL({ ~E{PF?H0K(RJA FJLmKm~EL Q<HvK I k?C+L Q<Fh4 Q<F��mFJQ]�% wlF?H;w ~EL({ ~E{PF?H;B<R?kJI(B<HWMONPF32 FJL QvRJL I�2 RJB�~�((wlF?H %j F Q@:mR?C+B 032 F0K(F�<>:mC/2 H@?BA �fRJQ�~�((wOMlH<H�~EL Q�w ~ :(MlRJB�~EB<k :(MlF�� K MOQ _ ImF�wlF?H�w ~EL({ ~E{PF?H%B<RJ{fI(wOMlFJB<H�H<C+L Q�MOLmkJwOImH

Km~ELmH wlF?H w ~EL({ ~E{PF?H MOLmK(RJA FJLmKm~EL Q<H K I�k?C+L Q<Fh4 Q<F��b_ I(MxH<C+L Q FJI54B� 2��32 F?H MOLmkJwOImH Km~ELmH wlF?H w ~EL({ ~E{PF?HK(RJA FJLmKm~EL Q<H3K I k?C+L Q<Fh4 Q<F�� k?F?H0K(FJBWL(MlFJB<H3RJQ�~EL Q�\mL ~EwlF32 FJL Q3MOLmkJwOImH.Km~ELmH0wlF?H;w ~EL({ ~E{PF?HvB<R?kJI(B<HWMONPF32 FJL QRJL I�2 RJB�~�((wlF?H %j F?H�w ~EL({ ~E{PF?H%B�~EQWMlC+L(LmFJwlH%C+I B<RJ{fI(wOMlFJB<H�C+L Q�I(LmF;H<QWBWImkJQWI(B<F�B<FJw ~EQWMONPF32 FJL Q HWM'2 A(wlF�FJQ�LmC+ImH%~EwOwlC+LmH%wlF?H

RJQWImK MlFJB.~EI A(B<Cqk : ~EMOL k : ~EA(MOQWB<F % j FJI(B<H.~+k?k?FJA(Q<FJI(B<H�� ~EA(A FJwlR?H.~EI(Q<C/2 ~EQ<F?H.K y RJQ�~EQ<H)\mL(M �(LmFxLmR?k?F?H<HWMOQ<FJL Q_ I y I(LmF+_ I ~EL QWMOQ<R \mL(MlFxK(F 2 R32 C+MOB<F�FJQ�wlFJI(B�B<F?k?C+L(L ~EMlH�H�~ELmk?F3A FJI(Q;H�F;Dz~EMOB<FxK(F 2 ~EL(M10JB<F3QWB 0?H;F>G kc~+k?F %j F?How ~EL({ ~E{PF?H MOLmK(RJA FJLmKm~EL Q<H K I'k?C+L Q<Fh4 Q<F _ I(M LmF H<C+L Q A ~+HoB<RJ{fI(wOMlFJB<HoLmR?k?F?H<HWMOQ<FJL Q K(F?HoB<F?k?C+L(L ~EMlH �H<FJI(B<H K MlHWA CfH^~EL QoK y I(LmF A(MOwlF A C+I(B,2 R32 C+BWMlH�FJB wlF k?C+L Q<Fh4qQ<F K(F B<FJQ<C+I(B ~EA(B 0?H w ~ B<F?k?C+L(L ~EMlH<H�~ELmk?F K IA ~EQWB<C+L k?C+I(B�~EL Q��wlFJI(B B<F?k?C+L(L ~EMlH<H�~ELmk?F A FJI(Q H<F Dz~EMOB<F K(F 2 ~EL(M10JB<F B<FJw ~EQWMONPF32 FJL Q F>G kc~+k?F��%HWI(BWQ<C+I(QA C+I(B;k?FJBWQ�~EMOLmF?H.kJw ~+H<H�F?H A ~EB@2 M�k?F?H�w ~EL({ ~E{PF?H _ ImF3LmC+ImH.RJQWImK MlFJB<C+LmH;A(wOImH�wlC+MOL RJ{ ~EwlF32 FJL Q %j F?H�w ~EL({ ~E{PF?H�K(RJA FJLmKm~EL Q<H K I k?C+L Q<Fh4 Q<F _ I(M LmFvH<C+L Q�A ~+H�MOLmK(RJA FJLmKm~EL Q<H�K I k?C+L Q<Fh4qQ<FvLmR?k?F?H<HWMOQ<FJL Q

A(wOImH�K(F0B<F?H<H�C+I(B<k?F?H�FJLmk?C+B<FvKm~ELmH%w ~,2 F?HWI(B<F.C$; w ~|B<F?k?C+L(L ~EMlH<H�~ELmk?F3K y I(LmF;A ~EBWQWMlFvK(F.k;: ~FElLmF0LmR?k?F?H�HWMOQ<FLmC+LoH<FJI(wlF32 FJL Q�K(F�k?C+LmH<FJBWNPFJB)wlF�k?C+L Q<Fh4qQ<F�NPFJB<H)wlF _ ImFJw C+LoK(C+MOQ)B<FJNPFJL(MOB�~EA(B 0?H)w ~;B<F?k?C+L(L ~EMlH�H�~ELmk?F��/2 ~EMlHLmR?k?F?H<HWMOQ<F ~EImH�HWM�wzy ~+k?k 0?H d K(F?HxMOL DGC+B@2 ~EQWMlC+LmH�HWI(B3wlF k?C+L Q<Fh4qQ<F Km~ELmHxwlF _ ImFJw�H�F5H<MOQWImF k?FJQWQ<F A ~EBWQWMlF K(Fk : ~FElLmF %5X L5\mLM� wlF?H�w ~EL({ ~E{PF?H�B<R?kJI(B<HWMONPF32 FJL Q;RJL I�2 RJB�~�((wlF?H H<C+L Q�K(F?H�w ~EL({ ~E{PF?H�A C+I(B�wlF?H _ ImFJwlH�C+L A FJI(QK(Rh\mL(MOB I(LmF A(B<Cqk?R?K I(B<F A FJB@2 FJQWQ�~EL Q K y RJL I�2 RJB<FJB B<R?kJI(B<HWMONPF32 FJL Q Q<C+I(Q<F?H wlF?H k;: ~FElLmF?H ~EA(A ~EBWQ<FJL ~EL Q~EI w ~EL({ ~E{PF % j F?H.w ~EL({ ~E{PF?H0B<R?kJI(B<HWMONPF32 FJL QxRJL I�2 RJB�~�((wlF?H+_ I(M LmF�H<C+L Q0A ~+H.K(RJA FJLmKm~EL Q<HvK I k?C+L Q<Fh4 Q<FH<C+L QvK MOQ<H! *># T� �6RP<9T �626%>)+*� A(I(MlH _ ImF�w ~ A(B<Cqk?R?K I(B<F K y RJL I�2 RJB�~EQWMlC+L#LmC+ImH3C / B<F�I(L 2 CPAPFJL#HWM'2 A(wlF5K(FNPRJBWMy\ FJB HWM I(LmFvk : ~FElLmFx~EA(A ~EBWQWMlFJL Q;~EI w ~EL({ ~E{PF�,qRJL I�2 RJB<FJB Q<C+I(Q<F?H�wlF?H�k : ~FElLmF?HU� ImH;_ I y d B<FJLmk?C+L QWB<FJB�w ~k : ~FElLmF d NPRJBWMy\ FJB %�^ ~Ew':mFJI(B<FJImH<F32 FJL Q��)k?FJQWQ<F A(B<Cqk?R?K I(B<F K y ~+k?k?FJA(Q�~EQWMlC+L�LmF A FJB@2 FJQ|A ~+H�K(F K(R?kJMlK(FJBHWM I(LmFok : ~FElLmFoL y ~EA(A ~EBWQWMlFJL Q�A ~+H|~EI w ~EL({ ~E{PFK, wlF w ~EL({ ~E{PF RJQ�~EL QxMOL5\mL(M � MOw LmF5H�FJB�~*�<~�2 ~EMlH3A CfH<HWM'((wlFK(F H�~cNPC+MOB HWM0w ~�k : ~FElLmF _ I(M0L y ~#A ~+H FJLmk?C+B<F RJQ<R C/((Q<FJL ImF wlF H�FJB�~ A(wOImH Q�~EB<K Km~ELmH wzy RJL I�2 RJB�~EQWMlC+LC+IN�<~�2 ~EMlH % j y ~+k?k?FJA(Q<FJI(B3A FJI(QvK(C+Lmk|B<RJA C+LmK B<F C+I(M)HWM w ~ k;: ~FElLmF ~EA(A ~EBWQWMlFJL Q|~EI w ~EL({ ~E{PF��2 ~EMlH0A FJI(Q( C+ImkJwlFJB;MOLmK(Rh\mL(M'2 FJL Q3HWM w ~ok : ~FElLmF�L y ~EA(A ~EBWQWMlFJL QvA ~+H0~EI w ~EL({ ~E{PF %

� ��

� �� T� e� � 8� ��

j F?H w ~EL({ ~E{PF?H DGC+B@2 FJwlH;K(C+L Q�w ~5HWQWBWImkJQWI(B<F|F?H<Q�w ~ A(wOImH�HWM'2 A(wlFxH�C+L Q�wlF?H w ~EL({ ~E{PF?H;K MOQ<H �PR� �) T * �� C+I�(2�8UTU'�@�@B*>) % pswmHWIHG Q�A C+I(B�B<F?k?C+L(L ~FElQWB<F;wlF?H%k : ~FElLmF?H�~EA(A ~EBWQ<FJL ~EL Q d I(L K(F;k?F?H�w ~EL({ ~E{PF?H%K(F0k?C+LmHWQWBWI(MOB<FI(L ~EI(Q<C/2 ~EQ<F \mL(M % f C+ImH ~EwOwlC+LmH NPC+MOB)Km~ELmH k?F�k;: ~EA(MOQWB<F%k?C/2L2 FJL Q H<C+L Q K(Rh\mL(MlH�k?F?H w ~EL({ ~E{PF?H��ak?C/2L2 FJL QC+L�A FJI(Q�k?C+LmH<QWBWI(MOB<F%I(Lo~EI(Q<C/2 ~EQ<F \mL(M B<F?k?C+L(L ~EMlH<H�~EL Q wlF?H�k : ~FElLmF?H�~EA(A ~EBWQ<FJL ~EL Q d I(L w ~EL({ ~E{PF d A ~EBWQWMOBK(F|H�~oK(Rh\mL(MOQWMlC+L %

� �� =56(@ � 2 / @ �� = #��z25=�:<-0=��;-��;4 �� ;25: � 4 �

r.~EA(A FJwlC+LmH _ ImF wlF?H w ~EL({ ~E{PF?H5DGC+B@2 FJwlH H<C+L Q5K(F?HoFJLmH<F32=((wlF?H K(F k;: ~FElLmF?H k?C+LmHWQWBWI(MOQ<F?HoHWI(B I(L'~Ewy�A�: ~�( FJQ K(C+L(LmR % rv~EA(A FJwlC+LmH RJ{ ~EwlF32 FJL Q w ~ _ ImF?HWQWMlC+L M'2 A C+BWQ�~EL Q<F#K(F H�~cNPC+MOB k?C/2L2 FJL Q K(Rh\mL(MOB FJLMOL Q<FJLmH<MlC+L I(L w ~EL({ ~E{PF3DGC+B@2 FJw % j F?H�w ~EL({ ~E{PF?H0B<RJ{fI(wOMlFJB<H.H<C+L Q.K(F?H;w ~EL({ ~E{PF?H�_ I(M A FJI(NPFJL Q.H�FxK(Rh\mL(MOB dA ~EBWQWMOBxK y I(L LmC/2=((B<F \mL(M)K(F5w ~EL({ ~E{PF?H3K(F ( ~+H<F5FJI54!� 2��32 F?H \mL(MlH�� FJQ3K y C+A RJB�~EQWMlC+LmHxFJLmH<F32=((wOMlHWQ<F?HxFJQK(F|k?C+Lmkc~EQ<RJL ~EQWMlC+L FJL QWB<F�k?F?H;w ~EL({ ~E{PF?H0FJQ;FJL QWB<F�wlF?H;k : ~FElLmF?Hv~EA(A ~EBWQ<FJL ~EL Q d k?F?H;w ~EL({ ~E{PF?H %

<�C+LmHWMlK(RJB<C+LmH I(L ~EwOA�: ~�( FJQ Σ = {a1, ...an}% c Rh\mL(MlH�H<C+LmH wlF?H w ~EL({ ~E{PF?H 8 ��T ��T 2 � � kc~EBp\mL(MlH FJQ

2��32 F|HWMOL({fwlFJQ<C+L � Li = {ai}% c Rh\mL(MlH<H<C+LmH0FJLmHWI(MOQ<FxwlF?H�QWB<C+MlH.C+A RJB�~EQWMlC+LmH.HWI(MON+~EL Q<F?H!,

GH�UI"�Q��-L ∪ L′ = {ω | ω ∈ L ou ω ∈ L′}

%kH�F��n�GHI M -

L · L′ = {u · v | u ∈ L et v ∈ L′}%

IKMPE��5M`I"�� !��mM`GU�F� nU�� "��!�U�� -L∗ =

⋃

i≥0Li�(C$;

L0 = {ε}

L1 = L

L2 = L · L1

...

Li+1 = L · Li

FJQ�w ~5DGFJB@2 FJQWI(B<FxA CfH<MOQWMONPF L+ =⋃

i>0Li<�F?H;H<FJI(wlF?H0C+A RJB�~EQWMlC+LmH;H<C+L Q;LmR?k?F?H<H�~EMOB<F?H0A C+I(B;k?C+LmH<QWBWI(MOB<F|wlF?H�w ~EL({ ~E{PF?H0B<RJ{fI(wOMlFJB<H!,

� �� E��QGU JI"�� - t L�w ~EL({ ~E{PF L ⊆ Σ∗ F?HWQ�K MOQ �PR� �) T * � � � 2�8UT '$@�@ *>) � HWM%FJQ�H<FJI(wlFh�2 FJL Q5H<M�MOw%A FJI(Q!�JQWB<F C/((Q<FJL I d A ~EBWQWMOB5K(F?H|w ~EL({ ~E{PF?H QWBWMON M ~EI54�HWI(B�wlF?H�H@AB2,( C+wlF?H�K(F ΣI(L(M1_ ImF32 FJL Q.A ~EB;wzy ~EA(A(wOMlkc~EQWMlC+L K(F?H.C+A RJB�~EQWMlC+LmH.K y I(L(MlC+LM�mK(FxA(B<CqK I(MOQ0FJQ;K(F3DGFJB@2 FJQWI(B<F %

$PZ j ~EL({ ~E{PF?H.B<RJ{fI(wOMlFJB<H0FJQ0~EI(Q<C/2 ~EQ<F?H�\mL(MlH

� �� %�� 4�6 6 �� =56 �� ;25: � � 4�6

. C+I(B)k?C+LmHWQWBWI(MOB<F�I(L w ~EL({ ~E{PF�B<RJ{fI(wOMlFJB�H<I(B I(L5~EwOA�: ~�( FJQ Σ �?MOw HWIHG Q�K(C+Lmk�K(F�A C+I(NPC+MOB k?C+LmHWQWBWI(MOB<F%wlF?Hw ~EL({ ~E{PF?H QWBWMONqM ~EI54 d A ~EBWQWMOB�K(F?H�H@A!2=( C+wlF?H K(F Σ A(I(MlH K(Fvk?C/2,((MOLmFJB wlF?H�w ~EL({ ~E{PF?H�A ~EB�K(F?H�C+A RJB�~EQWMlC+LmHK y I(L(MlC+LM�mK(F3A(B<CqK I(MOQ0FJQ;K(FvDGFJB@2 FJQWI(B<F % t LmFxFh4 A(B<F?H<HWMlC+L B<RJ{fI(wOM10JB<F�F?HWQ I(LmF|Fh4qA(B<F?H�HWMlC+L d w ~ 2 ~EL(M10JB<FK(F?H Fh4qA(B<F?H�HWMlC+LmH�~EBWMOQ@:�2 RJQWM1_ ImFb2 ~EMlH K(C+L Q�w ~.H<MO{fL(My\ kc~EQWMlC+L H<F�k?C/2 A(B<FJLmK FJL5Q<FJB@2 F?H�K y C+A RJB�~EQWMlC+LmH�HWI(BwlF?H|w ~EL({ ~E{PF?H % j F?H Fh4qA(B<F?H<H<MlC+LmH|B<RJ{fI(wOM10JB<F?HoH<C+L Q K(C+Lmk K(Rh\mL(MlF?H d wzy ~EMlK(F K y C+A RJB�~EQ<FJI(B<H�B<FJA(B<R?H�FJL Q�~EL QwlF?H�C+A RJB�~EQWMlC+LmH�A(B<R?k?R?K(FJL Q<F?H HWI(B�wlF?H%w ~EL({ ~E{PF?H FJQ�K(F)2 ~EL(M10JB<FvMOLmK ImkJQWMONPF0A C+I(B%B<F>O RJQ<FJB�wlFJI(B HWQWBWImkJQWI(B<FB<R?kJI(B<HWMONPF %

� qOkH�F�!�P�`I"�� FE!��GH "I"r!�F�.- � A ~EB;MOLmK ImkJQWMlC+L � nqC+MOQ Σ I(L ~EwOA�: ~�( FJQ�� ~EwlC+B<H� ∅ F?HWQ�I(LmFxFh4qA(B<F?H�HWMlC+L B<RJ{fI(wOM10JB<F�K(C+L Q;w ~oHWMO{fL(My\ kc~EQWMlC+L F?HWQ L(∅) = ∅� � ∈ Σ F?HWQ�I(LmF�Fh4qA(B<F?H<H<MlC+L B<RJ{fI(wOM10JB<F�K(C+L Q0w ~ HWMO{fL(My\ kc~EQWMlC+L F?HWQ L( � ) = { � }� nqC+MOQ e I(LmF Fh4qA(B<F?H�HWMlC+L B<RJ{fI(wOM10JB<F5K(RJLmC+Q�~EL Q L(e) � ~EwlC+B<H e � F?H<Q.~EImH<HWM�I(LmF|Fh4qA(B<F?H�HWMlC+LB<RJ{fI(wOM10JB<F�K(RJLmC+Q�~EL Q.wlF3w ~EL({ ~E{PF L(e)∗

� nqC+MlFJL Q e1FJQ e2

K(F?H3Fh4 A(B<F?H<HWMlC+LmHvB<RJ{fI(wOM10JB<F?HxK(RJLmC+Q�~EL QxwlF?Hvw ~EL({ ~E{PF?H L(e1)FJQ L(e2)

�~EwlC+B<He1e2

F?H<Q�I(LmFxFh4qA(B<F?H<H<MlC+L B<RJ{fI(wOM10JB<F�K(RJLmC+Q�~EL Q0wlF3w ~EL({ ~E{PF L(e1) · L(e2)e1 � e2

F?HWQ�I(LmFxFh4 A(B<F?H<HWMlC+L B<RJ{fI(wOM10JB<F K(RJLmC+Q�~EL Q0wlF3w ~EL({ ~E{PF L(e1) ∪ L(e2)

j F?H Fh4qA(B<F?H<H<MlC+LmH B<RJ{fI(wOM10JB<F?H LmC+ImH K(C+L(LmFJL Q I(L A(B<F32 MlFJB�2 C`APFJL A C+I(B Fh4qA(BWM'2 FJB K(F?H w ~EL({ ~E{PF?HDGC+B@2 FJwlH;FJL MOL Q<FJLmH<MlC+L %

� � � 2|@ � !�- @ 4�6��o= � 6

t L ~EI(Q<C/2 ~EQ<F�\mL(M�F?HWQoI(L 2 C K�0JwlF DGC+B@2 FJw�K(F kc~EwlkJI(w;K(C+L Q wlF k?C/2 A C+BWQ<F32 FJL Q F?HWQ5QWB 0?H HWM'2 A(wlF %� L wlF|B<FJA(B<R?H<FJL Q<F wlF|A(wOImH.H<C+I(NPFJL Qv{fB�~EA�:(M1_ ImF32 FJL Q3~cNPF?k K(F?H0L�3ImK(H _ I(M B<FJA(B<R?H<FJL Q<FJL Q3wlF?H0RJQ�~EQ<HvK(Fwzy ~EI(Q<C/2 ~EQ<F FJQxK(F?H O�0?k :mF?H|RJQWM1_ ImFJQ<R?H3A ~EB3I(L#H@A!2=( C+wlF _ I(M�B<FJA(B<R?H�FJL Q<FJL Q K(F?H3QWB�~ELmHWMOQWMlC+LmH3A CfH�HWM'((wlF?Hd A ~EBWQWMOBoK y I(L'k?FJBWQ�~EMOL'RJQ�~EQ K(F wzy ~EI(Q<C/2 ~EQ<F NPFJB<H5I(L'~EI(QWB<F wlC+B<H _ ImF wlF A(B<C k;: ~EMOL'H@A!2=( C+wlF Km~ELmHow ~k : ~FElLmF d NPRJBWMy\ FJB|k?C+BWB<F?H<A C+LmK d wzy RJQWM1_ ImFJQWQ<F HWI(Bxw ~&O�0?k :mF %�. ~EB@2 M�wlF?HxRJQ�~EQ<H|K(F5wzy ~EI(Q<C/2 ~EQ<F \mL(M � C+LK MlHWQWMOL({fImF.I(L RJQ�~EQ�MOL(MOQWM ~Ew FJQ�I(L FJLmH�F32,((wlFvK y RJQ�~EQ<H \mL ~EI54 % n M FJL A ~EBWQ�~EL Q�K(F0wzy RJQ�~EQ�MOL(MOQWM ~Ew �qC+L ~EBWBWMONPFd I(L RJQ�~EQ>\mL ~Ew A ~EB I(L HWI(MOQ<F3K(F.QWB�~ELmHWMOQWMlC+LmH�k?C+LmH<C/2L2 ~EL Q�I(L d I(L Q<C+ImH wlF?H�H A!2=( C+wlF?H K(F.w ~�k;: ~FElLmFK y FJL QWB<R?F�� ~EwlC+B<H;w ~ok;: ~FElLmF�F?HWQ;K MOQ<F�~+k?k?FJA(Q<R?F|A ~EB;wzy ~EI(Q<C/2 ~EQ<F %

j�G�MP��R�5MP� ST�HI�nUE�MP��/��IJ�UI"� MP� �@j� � � - I(L 2 �H8 '$#�2�8S*�� @�T$�6R 8S* ��# TA@�T >8S* F?HWQ|I(LmFH<QWBWImkJQWI(B<F (Q,Σ, δ, q0, F ) Q<FJwOwlF,_ ImF�,� Q F?HWQ�I(L FJLmH<F32=((wlF�\mL(M K y RJQ�~EQ<H�� Σ F?HWQ�I(L ~EwOA�: ~�( FJQvK y FJL QWB<R?F � \mL(M � �� δ : Q× Σ→ Q F?HWQ�I(LmF3DGC+LmkJQWMlC+L A ~EBWQWMlFJwOwlF K(FxQWB�~ELmHWMOQWMlC+L _ I(M �(RJQ�~EL Q.K(C+L(LmR|I(L RJQ�~EQ

qi ∈ Q FJQ�I(L H@AB2,( C+wlF a ∈ Σ � B<FJQ<C+I(BWLmF�I(L LmC+I(NPFJw RJQ�~EQ qj ∈ Q �� q0 ∈ Q F?HWQ�wzy RJQ�~EQ;MOL(MOQWM ~Ew�K(Fxwzy ~EI(Q<C/2 ~EQ<F�� FJQ� F ⊆ Q F?HWQ�wzy FJLmH<F32=((wlF�K(F?H.RJQ�~EQ<Hb\mL ~EI54 %�,�Q�Rk ��`MP�B�R�B�QM ��lml��kUMP�!GU� - nqC+MOQ (Q,Σ, δ, q0, F ) I(L ~EI(Q<C/2 ~EQ<F�\mL(M % n M d A ~EBWQWMOBK(F q0

� FJL'~EA(A(wOM1_ I ~EL Q HWImk?k?F?H<HWMONPF32 FJL QowlF?HoQWB�~ELmHWMOQWMlC+LmH K(Rh\mL(MlHoA ~EB δ HWI(B k : ~+kJI(L K(F?HH A!2=( C+wlF?H�K y I(LmF;k : ~FElLmF ω Km~ELmH%wzy C+B<K B<F��PC+L ~EBWBWMONPF;Km~ELmH%I(L RJQ�~EQ f ∈ F �P~EwlC+B<H�w ~3k;: ~FElLmFω F?HWQ;K MOQ<F=2 <P<7*S3 8SRP*oA ~EB;wzy ~EI(Q<C/2 ~EQ<F %

� qO�!�Rk� "� D �" <�C+LmHWMlK(RJB<C+LmH�wzy ~EI(Q<C/2 ~EQ<F A = ({q0, q1, q2, q3}, {0, 1}, δ, q0 , {q0})K(C+L Q�w ~|DGC+LmkJQWMlC+L

K(FxQWB�~ELmHWMOQWMlC+L δ F?HWQ;K(Rh\mL(MlF|A ~EB;w ~5Q�~�((wlF�HWI(MONf~EL Q<F&,

�5%87L[ I(Q<C/2 ~EQ<F?H \mL(MlH $&$

X L QWB<R?F?H� Q�~EQ<H Z $

q0 q2 q1

q1 q3 q0

q2 q0 q3

q3 q1 q2

<�FJQ0~EI(Q<C/2 ~EQ<F|F?HWQ�B<FJA(B<R?H<FJL Q<R|kJMy� K(F?H<H<C+ImH�Km~ELmH;H^~|DGC+B@2 F3{fB�~EA�:(M1_ ImF��mkfy F?HWQ � d � K MOB<F|H<C+ImH w ~ DGC+B@2 FK y I(L {fB�~EA�:mF C+BWMlFJL Q<R RJQWM1_ ImFJQ<R % j y RJQ�~EQ MOL(MOQWM ~Ew q0

F?HWQ HWMO{fL ~EwlR A ~EB wzy RJQWM1_ ImFJQWQ<F K(R3((I(Q FJQ w ~ O�0?k;:mFk?C+BWB<F?HWA C+LmKm~EL Q<F % j F?H QWB�~ELmHWMOQWMlC+LmH H�C+L Q B<FJA(B<R?H<FJL Q<R?F?H A ~EB I(LmF O�0?k;:mF K(C+L Q wzy C+BWMO{fMOLmF K(C+L(LmF wzy RJQ�~EQK(F K(RJA ~EBWQ�� wzy RJQWM1_ ImFJQWQ<F wzy FJL QWB<R?F k?C+LmH<C/2L2 R?F��FJQ�w ~ K(F?HWQWMOL ~EQWMlC+L�wzy RJQ�~EQ NPFJB<H|wlF _ ImFJw%LmC+ImH5~�2N0JLmF w ~DGC+LmkJQWMlC+L K(FxQWB�~ELmHWMOQWMlC+L % j F?H0RJQ�~EQ<Hb\mL ~EI54 H<C+L Q;B<FJA(B<R?H<FJL Q<R?F?H0A ~EB;I(L K(C+I�((wlF|k?FJB<kJwlF %

K(R3((I(Q //GFED@ABC?>=<89:;q0

1++

0

��

GFED@ABCq1

1

kk

0

��GFED@ABCq2

1++

0

TT

GFED@ABCq3

1

kk

0

TT

<�FJQ ~EI(Q<C/2 ~EQ<F ~+k?k?FJA(Q<F w ~ k;: ~FElLmF ω = 110101 ��A(I(MlH;_ I y FJL A ~EBWQ�~EL Q K(F wzy RJQ�~EQ q0�)w ~ k?C+LmH<C/2 �

2 ~EQWMlC+L�K I#A(B<F32 MlFJB|H@AB2,( C+wlF 1 LmC+ImH�~�2N0JLmF Km~ELmHxwzy RJQ�~EQ q1

% j F H<F?k?C+LmK#H@AB2,( C+wlF 1 LmC+ImH|B�~�2N0JLmFM'2L2 R?Km~EMOQ<F32 FJL Q�K(F�wzy RJQ�~EQ q1NPFJB<H�wzy RJQ�~EQ q0

% j ~xk?C+LmH<C/2L2 ~EQWMlC+L K(F?H�K(FJI54 H@AB2,( C+wlF?H%HWI(MONf~EL Q<H 0 A(I(MlH1 LmC+ImH�~�2N0JLmF.K(F�wzy RJQ�~EQ q0

NPFJB<H�wzy RJQ�~EQ q2A(I(MlH q3

%mX L k?C+LmH<C/2L2 ~EL Q FJLmHWI(MOQ<F0wlF?H�K(FJI54 K(FJBWL(MlFJB<H�H@AB2 �( C+wlF?H 0 A(I(MlH 1 � C+L B<FJNqMlFJL Q;K y ~�( C+B<K Km~ELmH�wzy RJQ�~EQ q1

�qA(I(MlH Km~ELmH q0

% j ~5k : ~FElLmF3F?HWQ�~EwlC+B<H�FJL QWM10JB<F32 FJL Qk?C+LmH<C/2L2 R?F�� FJQvwzy ~EI(Q<C/2 ~EQ<F F?HWQvKm~ELmHvwzy RJQ�~EQ q0

_ I(M F?HWQ.I(L RJQ�~EQ \mL ~Ew % � L�~+k?k?FJA(Q<FoK(C+Lmk w ~ k;: ~FElLmF110101

%2

j F k?C/2 A C+BWQ<F32 FJL Q ~+k?k?FJA(Q<FJI(B K(F wzy ~EI(Q<C/2 ~EQ<F LmC+ImH ~�2N0JLmF d A ~EBWwlFJB K(F w ~ LmC+QWMlC+L'K(F w ~EL({ ~E{PF~+k?k?FJA(Q<RxA ~EB;I(L ~EI(Q<C/2 ~EQ<F�,

� ��L��lml��kUMPE - wlF�w ~EL({ ~E{PF�~+k?k?FJA(Q<R�A ~EB I(L ~EI(Q<C/2 ~EQ<F>\mL(M A �!LmC+Q<R L(A) �+F?HWQ)wzy FJL5�H�F32,((wlF%K(F?H k : ~FElLmF?H ω ~+k?k?FJA(Q<R?F?H A ~EB A �?kfy F?H<Q � d � K MOB<F L(A) = {ω | ω F?HWQ0~+k?k?FJA(Q<R?F|A ~EB A}%

[ MOLmHWM � wlF|w ~EL({ ~E{PFo~+k?k?FJA(Q<R�A ~EB.I(L ~EI(Q<C/2 ~EQ<F,\mL(M)F?H<Q;I(L w ~EL({ ~E{PF�D C+B@2 FJw � A(I(MlH _ I y MOw�Hcy ~E{fMOQvK y I(LFJLmH<F32=((wlF K(F k : ~FElLmF?H H<I(B wzy ~EwOA�: ~�( FJQ K y FJL QWB<R?F#K(F wzy ~EI(Q<C/2 ~EQ<F %bX L Dz~EMOQ��wzy ~EI(Q<C/2 ~EQ<F#K(C+L(LmF I(LmFK(Rh\mL(MOQWMlC+L K MOQ<FD'>3 R �(2�8UTU'�@�@B*>)A)W* K(F k?F w ~EL({ ~E{PF��Km~ELmH w ~ 2 F?HWI(B<F C$;'MOw;K(Rh\mL(MOQ I(LmF A(B<Cqk?R?K I(B<F K(FK(R?kJMlHWMlC+L A C+I(B K MlHWQWMOL({fImFJB wlF?H�k : ~FElLmF?H�K I w ~EL({ ~E{PF L(A) K(F?H�~EI(QWB<F?H�k;: ~FElLmF?H k?C+LmHWQWBWImkJQWM'((wlF?H�HWI(B Σ∗ %j F?H.~EI(Q<C/2 ~EQ<F?H _ I(M�H<C+L Q0k?C+L DGC+B@2 F?H d w ~ K(Rh\mL(MOQWMlC+L A(B<R?k?R?K(FJL Q<F H�C+L Q0K MOQ<H �6R98S* �># T @�T >8S*> �kc~EB0w ~

DGC+LmkJQWMlC+L5K(F%QWB�~ELmHWMOQWMlC+L F?HWQ Q<FJwOwlF _ ImF%A C+I(B)k : ~/_ ImF�RJQ�~EQ��EHWI(B�I(LmF�FJL QWB<R?F�K(C+L(LmR?F��+C+L H�F�B<FJQWB<C+I(NPF Km~ELmH~EI A(wOImH I(L RJQ�~EQ � w ~ DGC+LmkJQWMlC+L K(F3QWB�~ELmHWMOQWMlC+L F?HWQ A ~EBWQWMlFJwOwlF��(MOw F?HWQ�K(C+Lmk3A CfH<HWM'((wlF+_ I y MOw L y A ~EMOQ�A ~+H;K(FQWB�~ELmHWMOQWMlC+L K(Rh\mL(MlF�A C+I(B)I(LoRJQ�~EQ�HWI(B)I(LmF FJL QWB<R?F�K(C+L(LmR?F �h% j F?H)Q@:mR?C+BWMlkJMlFJLmH�C+L Q RJ{ ~EwlF32 FJL Q%K(Rh\mL(M I(LmFDGC+B@2 F _ ImF K y ~EI(Q<C/2 ~EQ<F)_ ImF�wzy C+L kJB<CPA ~EMOQ�~vA(BWMlC+BWM(A(wOImH A(I(MlH<H^~EL Q<F��fwzy ~EI(Q<C/2 ~EQ<Fb\mL(M(LmC+L5� K(RJQ<FJB@2 MOLmH<Q<F %t L ~EI(Q<C/2 ~EQ<F)\mL(M LmC+L5� K(RJQ<FJB@2 MOL(MlHWQ<FvA FJB@2 FJQ�A(wOImHWMlFJI(B<H�QWB�~ELmHWMOQWMlC+LmH�NPFJB<H%K M0/ RJB<FJL Q<H RJQ�~EQ<H�K(FJA(I(MlH�I(LRJQ�~EQ K(C+L(LmR#FJQ HWI(B I(L�H@AB2,( C+wlF#K(C+L(LmR % c F A(wOImH�� MOw3A FJB@2 FJQ K(F?H QWB�~ELmHWMOQWMlC+LmH HWA C+L Q�~ELmR?F?H��H�~ELmHk?C+LmH<C/2L2 ~EQWMlC+L K(F|H@AB2,( C+wlFxK(Fxwzy FJL QWB<R?F�� ~EA(A FJwlR?F ε �zQWB�~ELmHWMOQWMlC+L %

j�G�MP��R�5MP� ST�UI ��Q��;nHEmMP�!��IJ�UI"� MP� �@j�� &- I(L 2 �8 '$#�2�8S* � @5T @Q'$@ ��6R98S* �># T @�T >8S*F?H<Q�I(LmF|HWQWBWImkJQWI(B<F (Q,Σ, δ, q0, F ) Q<FJwOwlF*_ ImF ,� Q F?HWQ�I(L FJLmH<F32=((wlF�\mL(M K y RJQ�~EQ<H��

$ � j ~EL({ ~E{PF?H.B<RJ{fI(wOMlFJB<H0FJQ0~EI(Q<C/2 ~EQ<F?H�\mL(MlH

�,��U� MP��GUl&MÌ"�� nJI1GH�� mqOkH�F�!�P�Ì"�� FE!��GH "I"r!�F� � kU��FMÌ"�pn I'GH�oj� � �

nqC+MOQ�I(L [ u�c M = (Q,Σ, δ, q0, F )% j y MlK(R?F F?HWQ�K(F k?C+LmHWQWBWI(MOB<F A ~EB|MOLmK ImkJQWMlC+L wlF?H|Fh4qA(B<F?H�HWMlC+LmH

B<RJ{fI(wOM10JB<F?H rkijK(RJLmC+Q�~EL Q;w ~oH<R _ ImFJLmk?FxK(FxH@AB2,( C+wlF?H�K(F Σ A FJB@2 FJQWQ�~EL QvK(FvDG~EMOB<FvA ~+H<H�FJB�wzy [ u�c MK(Fxwzy RJQ�~EQ i

d wzy RJQ�~EQ j H�~ELmH�A ~+H�H<FJB;A ~EB�I(L RJQ�~EQ0K y MOLmK Mlk?F|A(wOImH�{fB�~ELmK _ ImF k%

nqC+MOQ RkijwlF;w ~EL({ ~E{PF0B<F?k?C+L(L I A ~EB�wzy Fh4qA(B<F?H<H<MlC+L B<RJ{fI(wOM10JB<F rk

ij�fw ~|K(Rh\mL(MOQWMlC+L B<R?kJI(B<HWMONPFvK(F Rk

ijF?HWQ ,

R0ij =

{

{a|δ(qi, a) = qj}HWM i 6= j,

{a|δ(qi, a) = qj} ∪ {ε}HWM i = j,

Rkij = Rk−1

ik (Rk−1

kk )∗Rk−1

kj ∪Rk−1

ij

j F?H�Fh4 A(B<F?H<HWMlC+LmH B<RJ{fI(wOM10JB<F?H rkijK(RJLmC+Q�~EL Q%k?F?H�w ~EL({ ~E{PF?H�H<C+L Q�C/((Q<FJL ImH�HWM'2 A(wlF32 FJL Q�FJL ~EA(A(wOM1_ I ~EL Q

wlF?H;C+A RJB�~EQ<FJI(B<H0k?C+BWB<F?HWA C+LmKm~EL Q3~EI54 C+A RJB�~EQWMlC+LmH�Dz~EMOQ<F?H;HWI(B�wlF?H;w ~EL({ ~E{PF?H��mkfy F?HWQ � d � K MOB<F=,

r0ij = a1 + ... + ap si i 6= j

r0ij = a1 + ... + ap + ε si i = j

rkij = rk−1

ik (rk−1

kk )∗rk−1

kj + rk−1

ij

C$; {a|δ(qi, a) = qj} = {a1, ..., ap}%

�� 5%'$ � <�C+LmHWQWBWImkJQWMlC+L K y I(LmF|Fh4 A(B<F?H<HWMlC+L B<RJ{fI(wOM10JB<F d A ~EBWQWMOB.K y I(L [ u�c %

� Σ F?HWQ�I(L ~EwOA�: ~�( FJQvK y FJL QWB<R?F � \mL(M � �� δ : Q × Σ ∪ {ε} → 2Q F?H<QvI(LmF DGC+LmkJQWMlC+L A ~EBWQWMlFJwOwlF K(F QWB�~ELmH<MOQWMlC+LR_ I(M � RJQ�~EL Q|K(C+L(LmRI(L RJQ�~EQ qi ∈ Q FJQ5I(L H@AB2,( C+wlF a ∈ Σ C+I ε � B<FJQ<C+I(BWLmF I(L H<C+ImH � FJLmH<F32=((wlF K y RJQ�~EQ<HA CfH<H<M'((wlF?H Q′ ⊆ Q �

� q0 ∈ Q F?HWQ�wzy RJQ�~EQ;MOL(MOQWM ~Ew�K(Fxwzy ~EI(Q<C/2 ~EQ<F�� FJQ� F ⊆ Q F?HWQ�wzy FJLmH<F32=((wlF�K(F?H.RJQ�~EQ<Hb\mL ~EI54 %

j y I(QWMOwOMlH�~EQWMlC+L K y I(L ~EI(Q<C/2 ~EQ<FL\mL(M�LmC+L5� K(RJQ<FJB@2 MOL(MlHWQ<F F?HWQ|FJL Dz~EMOQ*((MlFJL#Q@:mR?C+BWM1_ ImF %UX L�F>/ FJQ�� HWI(BI(LmF5k : ~FElLmFoK(C+L(LmR?F�� wzy Fh4(R?kJI(QWMlC+L#K(F?H0QWB�~ELmH<MOQWMlC+LmH.LmR?k?F?H�HWMOQ<FJL Q d k;: ~/_ ImF5RJQ�~EA F k?F=_ ImF�wzy C+L ~EA(A FJwOwlFI(L k;:mC+My4�LmC+L5� K(RJQ<FJB@2 MOL(MlHWQ<F FJL QWB<F wlF?H�RJQ�~EQ<H5HWI(MONf~EL Q<H A CfH�HWM'((wlF?H � A#k?C/2 A(BWMlHok?FJI54�~+k?k?F?H<HWM'((wlF?H A ~EBε �zQWB�~ELmHWMOQWMlC+L �h% � L HWI(A(A CfH<F _ I y I(L8Q<FJw|k;:mC+My4�LmC+ImH ~�2N0JLmF d k : ~/_ ImF DGC+MlH NPFJB<H I(L8RJQ�~EQ Q<FJw*_ ImFHWMvw ~ k : ~FElLmF�K(C+MOQK�JQWB<F#~+k?k?FJA(Q<R?F��;C+L8~EBWMONPFJB�~ ( FJw3FJQ ((MlFJL8Km~ELmH I(L�RJQ�~EQ�\mL ~Ew % j F?H ~�2 RJBWMlkc~EMOLmH��((MlFJL A(B�~E{&2 ~EQWM1_ ImF?H�� ~EA(A FJwlFJB�~EMlFJL Q|k?FJw ~ K I �� T 74 � �) 8A46TA@�TA@ �� k?F _ I(M�A FJI(Q3Hcy ~EA(A ~EB<FJL Q<FJB d LmC+QWB<F�!A(B<FJLmK B<F|H<F?H�K(R?H<MOB<H�A C+I(B�K(F?H�B<Rc~EwOMOQ<R?H�� % <�C/2L2 FJL Q.FJL F>/ FJQ�B<Rc~EwOMlH�FJB;k?C+LmkJB 0JQ<F32 FJL QvI(L 2 R?kc~EL(MlH@2 F_ I(M.K(FJNf~EL Q A(wOImHWMlFJI(B<H ~EwOQ<FJBWL ~EQWMONPF?H k;:mC+MlHWMOB�~EMlFJL Q Q<C+I/�WC+I(B<H w ~ ( C+L(LmF � p w.L y Fh4qMlHWQ<F A ~+H K(F Dz~EMOQ K(F2 ~EL(M10JB<F;K(F�B<Rc~EwOMlH�FJB%k?FJw ~ 2 R?kc~EL(M1_ ImF32 FJL Q � MOL DGC+B@2 ~EQWM1_ ImF32 FJL Q � ~EI/�[C+I(B<K y : I(M % j y ~EI(Q<C/2 ~EQ<F�\mL(M(LmC+L5�K(RJQ<FJB@2 MOL(MlHWQ<F F?HWQ;K(C+LmkxI(L 2 CqK�0JwlF|K(F|kc~EwlkJI(w A(I(B<F32 FJL Q0Q@:mR?C+BWM1_ ImF %j F?H _ ImF?HWQWMlC+LmH.MOL Q<RJB<F?H<H^~EL Q<F?H+_ I(M�H<F�A CfH<FJL Q 2 ~EMOL Q<FJL ~EL Q|k?C+LmHWMlH<Q<FJL Q d H�~cNPC+MOBvK y I(LmF A ~EBWQ _ ImFJwOwlF

F?HWQxw ~ B<FJw ~EQWMlC+L FJL QWB<F wlF?Hxw ~EL({ ~E{PF?H|D C+B@2 FJwlH�K(Rh\mL(MlH|A ~EB|wlF?H|Fh4 A(B<F?H<HWMlC+LmH|B<RJ{fI(wOM10JB<F?H�� k?FJI54 _ I(M�H<C+L QK(Rh\mL(MlH�A ~EB%wlF?H ~EI(Q<C/2 ~EQ<F?H�K y RJQ�~EQ>\mL(MlH%K(RJQ<FJB@2 MOL(MlH<Q<F?H�FJQ�k?FJI54 FJL5\mL K(Rh\mL(MlH�A ~EB%wlF?H ~EI(Q<C/2 ~EQ<F?H>\mL(MlHLmC+L5� K(RJQ<FJB@2 MOL(MlHWQ<F?H %�� ~F�zQ �zMOw A ~EB@2 M�k?F?H D C+B@2 ~EwOMlH 2 F?H I(L _ I(M�H<C+MOQ5A(wOImH5A(I(MlH<H�~EL Q _ ImF wlF?H ~EI(QWB<F?H��j ~ B<RJA C+LmH<F.F?H<Q�LmC+L % k?F?H�QWB<C+MlH�D C+B@2 ~EwOMlH 2 F?H A FJB@2 FJQWQ<FJL Q;K(FvK(Rh\mL(MOB�Fh4m~+kJQ<F32 FJL Q;w ~,2��32 F3kJw ~+H<H<F3K(Fw ~EL({ ~E{PF?H�DGC+B@2 FJwlH��(wlF?H;w ~EL({ ~E{PF?H;B<RJ{fI(wOMlFJB<H %

�5%87L[ I(Q<C/2 ~EQ<F?H \mL(MlH $P7

�,�Q��PMP��GUl&M`I"�� nJI1GH� j�� kU��FM`I"�pn I1GU�U� ��qOkU��P�FIK�Q�o��E��QGU JI"r�� $&% . C+I(Bowzy Fh4qA(B<F?H<H<MlC+L�B<RJ{fI(wOM10JB<F ε � k?C+LmHWQWBWI(MOB<F wzy ~EI(Q<C/2 ~EQ<F N(ε) ~?NPF?k K(FJI54�RJQ�~EQ<H , I(L RJQ�~EQMOL(MOQWM ~Ew i FJQ|I(L�RJQ�~EQ,\mL ~Ew f � FJQ*A#K(Rh\mL(MOB|I(LmF H�FJI(wlF QWB�~ELmHWMOQWMlC+L H<I(B ε K(F i NPFJB<H f

%N(ε)B<F?k?C+L(L ~FElQ.wlFxw ~EL({ ~E{PF L = {ε}

%�5% . C+I(B wzy Fh4qA(B<F?H<H<MlC+L B<RJ{fI(wOM10JB<F a � C$; a ∈ Σ � k?C+LmHWQWBWI(MOB<Fvwzy ~EI(Q<C/2 ~EQ<F N(a) ~?NPF?kvK(FJI54 RJQ�~EQ<H ,I(L RJQ�~EQ|MOL(MOQWM ~Ew i FJQ�I(L RJQ�~EQ+\mL ~Ew f � FJQ*A#K(Rh\mL(MOB�I(LmF H<FJI(wlF QWB�~ELmHWMOQWMlC+L HWI(B a K(F i NPFJB<H

f%N(a) B<F?k?C+L(L ~FElQ;wlFxw ~EL({ ~E{PF L = {a}

%75% nqC+MlFJL Q N(s) FJQ N(t) K(FJI54 [ u�f A C+I(B�wlF?H;Fh4 A(B<F?H<HWMlC+L B<RJ{fI(wOM10JB<F?H s FJQ t �m~EwlC+B<H!,

� ~ � . C+I(B�wzy Fh4qA(B<F?H�HWMlC+L B<RJ{fI(wOM10JB<F s|t � k?C+LmHWQWBWI(MOB<Fvwzy ~EI(Q<C/2 ~EQ<F N(s|t) ~cNPF?kvI(L RJQ�~EQ MOL(MOQWM ~Ewi ~?NPF?k I(LmF QWB�~ELmHWMOQWMlC+L H<I(B ε NPFJB<H|wlF?H�RJQ�~EQ<H MOL(MOQWM ~EI54�K(F N(s) FJQ N(t) ��FJQ|I(L RJQ�~EQ\mL ~Ew f ~cNPF?kvI(LmF.QWB�~ELmH<MOQWMlC+L HWI(B ε K(F3k;: ~+kJI(L K(F?H�RJQ�~EQ<H \mL ~EI54 K(F?H�K(FJI54 ~EI(Q<C/2 ~EQ<F?HN(s) FJQ N(t)

% j y ~EI(Q<C/2 ~EQ<F N(s|t) B<F?k?C+L(L ~FElQ�~EMOLmHWM(wlF�w ~EL({ ~E{PF L(s|t) = L(s)∪L(t)%

� ( � . C+I(B wzy Fh4qA(B<F?H�HWMlC+L B<RJ{fI(wOM10JB<F st ��k?C+LmHWQWBWI(MOB<F wzy ~EI(Q<C/2 ~EQ<F N(st) ~cNPF?k k?C/2L2 F#RJQ�~EQMOL(MOQWM ~Ew i wzy RJQ�~EQ.MOL(MOQ�~Ew)K(F N(s) FJQ.k?C/2L2 F5RJQ�~EQ)\mL ~Ew wzy RJQ�~EQ�\mL ~Ew)K(F N(t) � FJL5\mLM� C+LD ImHWMlC+L(LmF;wzy RJQ�~EQ>\mL ~Ew K(F N(s) ~?NPF?k.wzy RJQ�~EQ%MOL(MOQWM ~Ew K(F N(t) � FJQ�k?FJQ�RJQ�~EQ%D ImH<MlC+L(LmR;A FJB<KH<C+L�H<Q�~EQWI(Q3K y RJQ�~EQ�\mL ~Ew�FJQ3MOL(MOQWM ~Ew�Km~ELmH N(st)% j y ~EI(Q<C/2 ~EQ<F N(st) B<F?k?C+L(L ~FElQ ~EMOLmHWMwlFxw ~EL({ ~E{PF L(st) = L(s)L(t)

%� k � . C+I(B�wzy Fh4 A(B<F?H<HWMlC+L B<RJ{fI(wOM10JB<F s∗ � k?C+LmHWQWBWI(MOB<F.wzy ~EI(Q<C/2 ~EQ<F N(s∗) ~?NPF?k.I(L RJQ�~EQ�MOL(MOQWM ~Ew iFJQ I(L RJQ�~EQ>\mL ~Ew f �(~F�[C+I(Q<FJB I(LmF.QWB�~ELmHWMOQWMlC+L HWI(B ε K(F i NPFJB<H�wzy RJQ�~EQ MOL(MOQWM ~Ew K(F N(s) FJQNPFJB<H f � ~F�WC+I(Q<FJB|~EImH<HWM I(LmF QWB�~ELmHWMOQWMlC+L#HWI(B ε K(F�wzy RJQ�~EQ \mL ~Ew�K(F N(s) NPFJB<H f � FJL5\mLM�~F�WC+I(Q<FJB|I(LmF QWB�~ELmHWMOQWMlC+L HWI(B ε K(Fowzy RJQ�~EQ,\mL ~Ew%K(F N(s) NPFJB<Hxwzy RJQ�~EQ|MOL(MOQWM ~Ew%K(F N(s)

%j y ~EI(Q<C/2 ~EQ<F N(s∗) B<F?k?C+L(L ~FElQ.~EMOLmHWM wlF3w ~EL({ ~E{PF L(s∗) =

⋃∞i=0

L(s)i %

�� 5% � � <�C+LmHWQWBWImkJQWMlC+L K(F+ab:mC/2 AmH<C+L %

� UE��FrB�R� D �J � R�� T �F2�)W*>@B<7* �� B'$TU8 L �@ )W2$@62�6* 2 <P<7* 3B8SR 3H2 � �@ �� A � 2�)0' �� T )* $T >8S* �@B* * �3��P*� � �T '$@ �(R � ) T�� (* e 8S*9) )+*�� * L(A) = L(e) �

� ��!G �� j ~ A(B<FJI(NPFxF?HWQ�A ~EB;k?C+LmHWQWBWImkJQWMlC+L % � L 2 C+L QWB<FxK y I(LmF3A ~EBWQ�k?C/2L2 FJL Q0k?C+LmHWQWBWI(MOB<F3I(L ~EI(Q<C��2 ~EQ<F \mL(M K(RJQ<FJB@2 MOL(MlHWQ<F d A ~EBWQWMOB K y I(LmF�Fh4qA(B<F?H<H<MlC+L B<RJ{fI(wOM10JB<F � NPC+MOB�w ~ \m{fI(B<F �5%87 �h% � L 2 C+L QWB<F�FJLmHWI(MOQ<Fk?C/2L2 FJL Q k?C+LmHWQWBWI(MOB<F I(LmFoFh4qA(B<F?H�HWMlC+L#B<RJ{fI(wOM10JB<F d A ~EBWQWMOB|K y I(L�~EI(Q<C/2 ~EQ<F \mL(M � NPC+MOBxw ~p\m{fI(B<F �5%'$��h%��

� UE��FrB�R� D � D � R�� T �F2�)W*>@B<7* �� B'$TU8 L �@ )W2$@ 2�6*&26<P<7*S3B8SR:3 2 � � @ �� A � 2�)0' �� T )* $T >8S* �@ �� A′ 8S*>)�� * L(A) = L(A′) �

� ��!G �� X Lmk?C+B<F I(LmF DGC+MlH�w ~ A(B<FJI(NPF F?HWQ5A ~EBok?C+LmH<QWBWImkJQWMlC+L %T. ~EB K(Rh\mL(MOQWMlC+LM� Q<C+I(Q ~EI(Q<C/2 ~EQ<F�\mL(MK(RJQ<FJB@2 MOL(MlHWQ<F�A FJI(Q �JQWB<F%Q�~ELmHWD C+B@2 R�FJL5~EI(Q<C/2 ~EQ<F>\mL(M LmC+L5� K(RJQ<FJB@2 MOL(MlHWQ<F C$; w ~ DGC+LmkJQWMlC+L5K(F%QWB�~ELmHWMOQWMlC+LB<FJQ<C+I(BWLmF Q<C+I/�WC+I(B<H I(L�HWMOL({fwlFJQ<C+L8C+I I(L FJLmH�F32,((wlF�K y RJQ�~EQ<H NqMlK(F % � L 2 C+L QWB<F#FJLmHWI(MOQ<F#k?C/2L2 FJL QQWB�~ELmH[DGC+B@2 FJB�Q<C+I(Q ~EI(Q<C/2 ~EQ<FN\mL(M�LmC+L5� K(RJQ<FJB@2 MOL(MlHWQ<F FJL ~EI(Q<C/2 ~EQ<FL\mL(M�K(RJQ<FJB@2 MOL(MlHWQ<F % j y MlK(R?F K(F w ~k?C+LmHWQWBWImkJQWMlC+L F?H<Q�w ~oH<I(MON+~EL Q<F % j y ~EI(Q<C/2 ~EQ<F|K(RJQ<FJB@2 MOL(MlHWQ<F|F?H<Q C/((Q<FJL I FJL A(B<FJL ~EL Q.k?C/2L2 FxRJQ�~EQ<H;K(F?HH<C+ImH � FJLmH�F32,((wlF?HvK y RJQ�~EQ<H.K(F�wzy ~EI(Q<C/2 ~EQ<F�LmC+L5� K(RJQ<FJB@2 MOL(MlHWQ<F % j F?H.QWB�~ELmHWMOQWMlC+LmHvK(Fxwzy [ u�c HWM'2 I(wlFJL QxFJLA ~EB�~EwOw10JwlF Q<C+I(Q<F?H�wlF?H QWB�~ELmHWMOQWMlC+LmH _ I(M�RJQ�~EMlFJL Q5A CfH<H<M'((wlF?H�FJL QWB<F wlF?H5RJQ�~EQ<H�K(F wzy [ u�f MOLmkJwOImH Km~ELmH I(Lk?FJBWQ�~EMOL RJQ�~EQ K(F wzy [ u�c FJL A(B<C K I(MlH�~EL Q k?C/2L2 F LmC+I(NPFJw;RJQ�~EQ wlF H<C+ImH � FJLmH<F32=((wlF K(F Q<C+ImHowlF?H RJQ�~EQ<H~EQWQ<FJMOL Q<H.Km~ELmH;wzy [ u�f % ��

$3] j ~EL({ ~E{PF?H.B<RJ{fI(wOMlFJB<H0FJQ0~EI(Q<C/2 ~EQ<F?H�\mL(MlH

�,��U� MP��GUl&MÌ"�� nHI"��l&MP� nU� I'j� � � �P��U�NkU��`�P��kU�� GH� j��

nqC+MOQ r I(LmFxFh4qA(B<F?H<H<MlC+L B<RJ{fI(wOM10JB<F��mwzy ~EwO{PC+BWMOQ@:�2 F�{PRJLmRJB�~Ew F?HWQ:,$&% <�C+LmH<QWBWI(MOB<F|I(L ~EB@((B<F�~�(mHWQWB�~EMOQ0A C+I(B;wzy Fh4 A(B<F?H<HWMlC+L B<RJ{fI(wOM10JB<F � B ��5% � QWM1_ ImFJQ<FJB.wlF?H�L�3ImK(H0K(Fxk?FJQ.~EB@((B<F ~�(mHWQWB�~EMOQ0k?C+L Q<FJL ~EL QvK(F?H0H@A!2=( C+wlF?H0K y FJL QWB<R?F75% < ~EwlkJI(wlFJB.wlF?H)_ I ~EQWB<F3D C+LmkJQWMlC+LmH � @�@��)02 %>)W* �� P*># T � �P*�� '$ >� � * �>@�T�� (*�� ' FJQ�� '$ � �T � 2$@58S*]�% <�C+LmH<QWBWI(MOB<F|wzy [ uHcgd wzy ~EMlK(F|K(F|w ~ D C+LmkJQWMlC+L�� ' �� T �F2$@58S*�,�� "l�GU nH��N� ��Ul&MÌ"��U�� m��! ��#"�$ �mM&%'�(�)��! ��#"�$j F?H�D C+LmkJQWMlC+LmH � @5@�� )W26%>)+* FJQ*� �P*># T � �P*�� '$ �H�C+L Q�K(Rh\mL(MlF?H)A ~EB)MOLmK ImkJQWMlC+L HWI(B)wlF?H)L�3ImK(H K(F%wzy ~EB@((B<F~�(mHWQWB�~EMOQ0K(Fxwzy Fh4 A(B<F?H<HWMlC+L B<RJ{fI(wOM10JB<F H<FJwlC+L wlF?H�B 0J{fwlF?H0HWI(MON+~EL Q<F?H!,

f �3ImK n � @�@��)026%9)W* � @ � � �(*># T�� P*�� ' � @ �DGFJI(MOwOwlF|RJQWM1_ ImFJQ<R?F ε

�O�F��I∅D FJI(MOwOwlF|RJQWM1_ ImFJQ<R?F i

��G�q{i}L�3ImK RJQWM1_ ImFJQ<R | � @�@��)02 %>)W* � c1

� � �P*># T � �P*�� '$ � c1�

K(F�\mwlH c1FJQ c2

��G � @�@��)W26%>)+* � c2� ∪ � �(*9# T�� P*�� ' � c2

��Ì � @�@��)W26%>)+* � c1� �� "��

L�3ImK RJQWM1_ ImFJQ<R • � @�@��)02 %>)W* � c1� � �P*># T � �P*�� '$ � c1

�K(F�\mwlH c1

FJQ c2

��M � @�@��)02 %>)W* � c2� ∪ � �(*9# T�� P*�� ' � c2

��ÌJ�U�� (*># T�� P*�� ' � c1�

L�3ImK RJQWM1_ ImFJQ<R ∗ �O�F��I � �(*9# T�� P*�� ' � c1�

K(F \mwlH c1

��*��@�T�� P*�� ' 5F?HWQ;kc~EwlkJI(wlR?F�k?C/2L2 F�� (*># T�� P*�� ' oFJL MOL Q<FJBWNPFJBWQWMlH<H�~EL Q.wlF?H;B��+wlF?H0K(F c1FJQ c2

%�,�� "l�GU nH� "� ��Q��lmMÌK�Q�+�#"�$-,� ��/.0�1�2��c FJI54 B 0J{fwlF?H.HWIHG H<FJL Q d kc~EwlkJI(wlFJB0w ~ DGC+LmkJQWMlC+L3� ' � � T �F2$@Q8S*&,

$&% n M @ F?HWQ I(L L�3ImK RJQWM1_ ImFJQ<R A ~EB • K(F�\mwlH c1FJQ c2

FJQ HWM i F?HWQ I(LmF A CfHWMOQWMlC+L Km~ELmH� * �>@�T ��(*��' � c1

� � ~EwlC+B<H Q<C+I(Q<F?H wlF?H A CfH<MOQWMlC+LmH�K(F4� �P*># T�� (*�� ' � c2��~EA(A ~EBWQWMlFJL(LmFJL Q d � '$ �

� �T �F2$@58S* � T � %�5% n M @ F?H<Q5I(L'L�3ImK'RJQWM1_ ImFJQ<R A ~EB ∗ FJQ i F?H<Q5I(LmF A CfHWMOQWMlC+L Km~ELmH � * ��@5T � �P*�� '$ � @ � ��~EwlC+B<HQ<C+I(Q<F?H0wlF?H�A CfH<MOQWMlC+LmH;Km~ELmH5� �P*># T�� (*�� ' � @ �5H�C+L Q0Km~ELmH��' � �T �F2$@58S* � T � %

�,��U� MP�/G�l&MÌ"�Q�onH� I1j � �$&% �56 8 2�8A &,87:9-� �(*9# T�� P*�� ' � �(2 <9TA@B* �);

�5% MP��QM��OG�� MOw Fh4qMlH<Q<FxKm~ELmH ��6 8 2�8A � @DR98 2�8 @Q'$@ �S#�2 �� R T < �1�=��75% 2 ~EB _ ImFJB T]�% k �QG�� k : ~/_ ImF|H@AB2,( C+wlFxK(Fxwzy ~EwOA�: ~�( FJQ a ∈ Σ� ��I"�F�

-5% H<C+MOQ U wzy FJLmH<F32=((wlF�K(F?H�A CfHWMOQWMlC+LmH _ I(M ~EA(A ~EBWQWMlFJL(LmFJL Q d � '$ � �T � 2$@58S* � 3 ��A C+I(B;I(LmFA CfHWMOQWMlC+L p K(F T Q<FJwOwlF*_ ImF3wlF�H@A!2=( C+wlFxFJL A CfHWMOQWMlC+L p H�C+MOQ a

%65% �Ì

U L y F?HWQ�A ~+H0N MlK(FxFJQ;L y ~EA(A ~EBWQWMlFJL Q0A ~+H d ��6 8 2 8A �� K��F�CB% ~F�WC+I(Q<FJB U k?C/2L2 F�RJQ�~EQ;LmC+L5� 2 ~EB _ ImR d ��6 8 2�8A �5% �?> �(2$@�@A> � 2CB=,87 UST�

ST�

�� 5%87 � <�C+LmHWQWBWImkJQWMlC+L K MOB<F?kJQ<F|K y I(L [ uHcgd A ~EBWQWMOB0K y I(LmF�Fh4qA(B<F?H<H<MlC+L B<RJ{fI(wOM10JB<F %

�5%87L[ I(Q<C/2 ~EQ<F?H \mL(MlH $P-

�,��U� MP�/G�l&MÌ"�Q�on I'GH� j� � � kH��`MÌ"�pn I1GU� j ��

�,�� "l�GU nH�ε−fermeture(T )nqC+MOQ T I(L FJLmH<F32=((wlF5K y RJQ�~EQ<HvK(F|wzy [ u�f � kc~EwlkJI(wlFJB.wzy FJLmH�F32,((wlF5K(F?H.RJQ�~EQ<Hvk?C/2 A(B<FJL ~EL Q T FJQ0Q<C+ImH

wlF?H;RJQ�~EQ<H.~EQWQ<FJMO{fL ~�((wlF?H.K(FJA(I(MlH;I(L RJQ�~EQ.K(F T A ~EB;I(LmF|C+I A(wOImHWMlFJI(B<H0QWB�~ELmHWMOQWMlC+LmH0HWI(B ε%

$&%X 2 A(MOwlFJB0Q<C+ImH�wlF?H.RJQ�~EQ<H;K(F T Km~ELmH 3QTA)+*�5% MOL(MOQWM ~EwOMlH�FJB ε−fermeture(T )

dT75% MP��QM��OG�� 3QT )+* F?HWQ�LmC+L5�zNqMlK(F ��I"��]�% K(RJA(MOwlFJB t wlFxH<C/2L2 FJQ0K(F 3BT )+*-5% k �QG�� k : ~/_ ImF|RJQ�~EQ u ~cNPF?kxI(L ~EB<kxK(F t

du RJQWM1_ ImFJQ<RxA ~EB ε � ��I"�F�65% ~F�[C+I(Q<FJB u

dε−fermeture(T )CB% F32 A(MOwlFJB u HWI(B 3QT )+*ST�

ST�j� "��/I M� H�R� nU� lm��U� MP�/G�l&MÌ"�Q�onH� I1j � �j ~ 2 RJQ@:mCqK(FxI(QWMOwOMlH<R?F|k?C+LmH<MlHWQ<F d k?C+LmHWQWBWI(MOB<F�wlF?H;RJQ�~EQ<H0K(F3wzy [ u�c k?C/2L2 F|K(F?H;FJLmH<F32=((wlF?H.K y RJQ�~EQ<HK(F wzy [ uHf � FJQ5K(F k?C+LmHWQWBWI(MOB<F w ~ D C+LmkJQWMlC+L K(F QWB�~ELmHWMOQWMlC+L FJL QWB<F k?F?H RJQ�~EQ<H�K(F Q<FJwOwlFoDG~$�?C+L _ I y FJwOwlFHWM'2�I(wlF#FJL�A ~EB�~EwOw10JwlF Q<C+I(Q<F?H wlF?H QWB�~ELmHWMOQWMlC+LmH A CfH<HWM'((wlF?H Km~ELmH wzy [ uHf % � L N+~ K(C+Lmk#k?C+LmHWQWBWI(MOB<F��6 8 2�8A �FJQ �?> � 2�@ >��B<F?HWA F?kJQWMONPF32 FJL Q wzy FJLmH<F32,((wlF�K(F?H RJQ�~EQ<H FJQ w ~�DGC+LmkJQWMlC+L K(F QWB�~ELmHWMOQWMlC+L K(Fwzy [ u�c % nqC+MOQ e0

wzy RJQ�~EQ MOL(MOQWM ~Ew3K(F wzy [ uHf ��wzy ~EwO{PC+BWMOQ@:�2 F K(F kc~EwlkJI(wvK(F ε−fermeture(T ) FJQ w ~D C+LmkJQWMlC+L Transiter(T, a) _ I(M�B<FJQ<C+I(BWLmF Q<C+ImH wlF?H5RJQ�~EQ<H K(F wzy [ u�f NPFJB<H wlF?H _ ImFJwlH�MOw�Fh4qMlHWQ<F I(LmFQWB�~ELmHWMOQWMlC+L HWI(B a K(FJA(I(MlH;I(L RJQ�~EQ.K(F T ,$&%[ I K(RJA ~EBWQ�� 56 8 2�8A �k?C+L QWMlFJL Q.I(L H<FJI(w RJQ�~EQ;MOL(MOQWM ~Ew LmC+L5� 2 ~EB _ ImR ε−fermeture(e0)

�5% MP��QM��OG�� MOw Fh4qMlH<Q<F3I(L RJQ�~EQ;LmC+L5� 2 ~EB _ ImR T Km~ELmH �56 8 2�8A ��I"��75% 2 ~EB _ ImFJB T]�% k �QG�� k : ~/_ ImF|H@AB2,( C+wlFxK y FJL QWB<R?F a ∈ Σ� ��IK��

-5%U ,87 ε−fermeture(Transiter(T, a))65% �Ì

U L y ~EA(A ~EBWQWMlFJL QvA ~+H d �56 8 2�8A �� "��CB% ~F�WC+I(Q<FJB U k?C/2L2 F�RJQ�~EQ;LmC+L5� 2 ~EB _ ImR d c � Q�~EQ<H�5%

DTran[T, a] ,87 UST�ST�

�� 5% ] � <�C+LmHWQWBWImkJQWMlC+L K y I(L [ u�c R _ I(MONf~EwlFJL Q d I(L [ u�f %

�,�� J "��I"�F� D �J � R�� T �F2�)W*>@B<7* �� B'$TU8 L � @ )02�@ 2�6* 2 <7<7*S3B8SR&3 2 � � @ �� A � 2$)W' �� KT )* $T >8S* �@B* * �3��P*� � �T '$@ �(R � ) T�� (* e 8S*9) )+*�� * L(A) = L(e) �

� ��!G �� c R?k?C+I(wlFoK MOB<F?kJQ<F32 FJL Q|K I Q@:mR?C+B 032 F5K y R _ I(MONf~EwlFJLmk?F [ u�c�� [ u�f FJQ3K I Q@:mR?C+B 032 FoK y R _ I(My�Nf~EwlFJLmk?F [ u�c�� X r % �� j y R _ I(MONf~EwlFJLmk?F0FJL QWB<F;Fh4 A(B<F?H<HWMlC+LmH�B<RJ{fI(wOM10JB<F?H�FJQ%~EI(Q<C/2 ~EQ<F?H \mL(MlH%K(RJQ<FJB@2 MOL(MlHWQ<F?H�F?H<Q�Fh4qQWBP�32 F32 FJL QM'2 A C+BWQ�~EL Q<F;FJLoA(B�~EQWM1_ ImF��fkc~EB k?FJw ~vNPFJI(Q�K MOB<F _ ImF�wlF?H w ~EL({ ~E{PF?H�K(Rh\mL(MlH�A ~EB wlF?H�Fh4qA(B<F?H<H<MlC+LmH B<RJ{fI(wOM10JB<F?HA FJI(NPFJL Q��JQWB<F3~+k?k?FJA(Q<R?H�A ~EB�K(F?H A(B<C+{fB�~�2L2 F?H0k?C+LmH<C/2L2 ~EL Q�A FJI K(FvB<F?H<H�C+I(B<k?F?H ,qI(LmF�_ I ~EL QWMOQ<R \mL(MlFK(F�2 R32 C+MOB<F A C+I(B I(L w ~EL({ ~E{PF K(C+L(LmR % f C+ImHo~EwOwlC+LmH NPC+MOB ~EI A(B<C k;: ~EMOL k;: ~EA(MOQWB<F d _ ImFJw�A C+MOL Q5wlF?Hw ~EL({ ~E{PF?H;B<RJ{fI(wOMlFJB<H0A FJI(NPFJL Q0LmC+ImH�B<FJLmK B<F�K(FxA(B<R?kJMlFJI54 H<FJBWN Mlk?F?H %

$P6 j ~EL({ ~E{PF?H.B<RJ{fI(wOMlFJB<H0FJQ0~EI(Q<C/2 ~EQ<F?H�\mL(MlH

j y M'2 A C+BWQ�~ELmk?F K(F w ~�H<F?k?C+LmK(F R _ I(MONf~EwlFJLmk?F��%FJL QWB<F [ uHc FJQ [ u�f ��F?HWQN2 C+MOLmH M'2L2 R?K M ~EQ<F32 FJL QNqMlHWM'((wlF %tX L DG~EMOQ�� MOw�F?HWQ.A(wOImHxH<M'2 A(wlF K(FokJB<R?FJB3I(L�~EI(Q<C/2 ~EQ<F \mL(M)LmC+L5� K(RJQ<FJB@2 MOLmH<Q<F A ~EB.w ~�2 RJQ@:mCqK(FK(F�ab:mC/2 AmH<C+L _ ImFvK(F3kJB<R?FJB;K MOB<F?kJQ<F32 FJL Q;I(L ~EI(Q<C/2 ~EQ<F \mL(M K(RJQ<FJB@2 MOL(MlHWQ<F % <�FJBWQ�~EMOLmH�wlC+{fMlkJMlFJwlH;k;:mC+My�HWMlH<H�FJL Q%K(C+Lmk.K(F�A ~+H<H<FJB�A ~EB%I(L ~EI(Q<C/2 ~EQ<F;LmC+L5� K(RJQ<FJB@2 MOL(MlHWQ<F % j F0K(RiDG~EI(Q�k?FJA FJLmKm~EL Q�K I A ~+H<H^~E{PF�A ~EBI(L ~EI(Q<C/2 ~EQ<F \mL(MqLmC+L5� K(RJQ<FJB@2 MOL(MlHWQ<F F?HWQ w ~0Q�~EMOwOwlF�K(F�wzy ~EI(Q<C/2 ~EQ<F>\mL(MqK(RJQ<FJB@2 MOL(MlH<Q<F�A(B<CqK I(MOQ %�X L5F>/ FJQ��wlF?H RJQ�~EQ<H K(F0wzy [ u�c A(B<CqK I(MOQ�A ~EB wzy ~EwO{PC+BWMOQ@:�2 FxK(F.w ~+\m{fI(B<F �5% ] RJQ�~EL Q;K(F?H H<C+ImH � FJLmH�F32,((wlF?H�K(F?H RJQ�~EQ<HK(F.wzy [ u�f �PwlF;LmC/2=((B<FvA C+Q<FJL QWMlFJw K y RJQ�~EQ<H K(F0wzy [ u�c A FJI(Q�~EwOwlFJBU�[ImH _ I y ~EI LmC/2,((B<F3K(FvH<C+ImH � FJLmH<F32=((wlF?HK(F wzy FJLmH<F32,((wlF K(F?HoRJQ�~EQ<H K(F wzy [ u�f ��_ I(M�F?HWQ5Fh4qA C+LmFJL QWMlFJw A(I(MlH _ ImF wlF LmC/2,((B<F K(F H<C+ImH � FJLmH<F32=((wlF?HK y I(L FJLmH<F32=((wlF�K(F3Q�~EMOwOwlF n F?HWQ 2n %p wvL y A ~ k?FJA FJLmKm~EL Q A ~+H K y I(L(MlkJMOQ<R#K y ~EI(Q<C/2 ~EQ<F \mL(M3K(RJQ<FJB@2 MOL(MlHWQ<F A C+I(B ~+k?k?FJA(Q<FJB I(L�k?FJBWQ�~EMOL

w ~EL({ ~E{PF L%b[ I k?C+L QWB�~EMOB<F��A(wOImHWMlFJI(B<H ~EI(Q<C/2 ~EQ<F?H A FJI(NPFJL Q B<F?k?C+L(L ~FElQWB<F#I(L 2��32 F w ~EL({ ~E{PF % t LmF

kc~EB�~+kJQ<RJBWMlHWQWM1_ ImF#M'2 A C+BWQ�~EL Q<F�K(F?H ~EI(Q<C/2 ~EQ<F?H F?HWQ ((MlFJL8H��(B wlFJI(B Q�~EMOwOwlF#FJL�LmC/2,((B<F�K y RJQ�~EQ<H % pswxH<FQWB<C+I(NPFL_ ImF A ~EB@2 M�Q<C+ImH|wlF?H|~EI(Q<C/2 ~EQ<F?H*_ I(M A FJI(NPFJL QxB<F?k?C+L(L ~FElQWB<F I(L 2��32 Fow ~EL({ ~E{PF�� MOw�Fh4 MlHWQ<F5I(L~EI(Q<C/2 ~EQ<F*2 MOL(M'2 ~Ew I(L(M1_ ImF�~EI B<FJLmC/2L2 ~E{PF�K(FxH<F?H;RJQ�~EQ<H;A(B 0?H %� UE��FrB�R� D �1i � �� # TA@�T #�2$) � 3H2 �># T 8 ' �6 )W*� �� P*(<P'�@�@Q2$T 7 2$@58 �@1#��>#&* )02�@ 2�6* L � TA) *9@* $T >8S* � @ �� @ �P*>@Q'$# #�2�6* �6* �*� R98 2 8A J3�� 3H'$ 7 R�� 2$@58 )+*J3Q) � J3 * 8UTA8 @Q'�#�%��(*�� R 8 2�8A @ R(<7*� � 92$T �(*3H' �� P*(<P'$@5@Q2$?U8 �(* L �

� ��!G �� X Lmk?C+B<F I(LmFoDGC+MlH�� w ~ A(B<FJI(NPF K(F k?F Q@:mR?C+B 032 F F?HWQ�C/((Q<FJL ImF A ~EB5k?C+LmHWQWBWImkJQWMlC+L % j y MlK(R?F K(Fwzy ~EwO{PC+BWMOQ@:�2 F.A(B<R?H<FJL Q<R d w ~�\m{fI(B<F �5%8- k?C+LmHWMlH<Q<F d k?C+LmHWQWBWI(MOB<F.wzy ~EI(Q<C/2 ~EQ<F 2 MOL(M'2 ~Ew A ~EB�K(F?H�RJQ�~EQ<H>_ I(MH<C+L Q�K(F?H%kJw ~+H�H<F?H%K y R _ I(MON+~EwlFJLmk?F?H�HWI(B�wlF?H�RJQ�~EQ<H�K(F;wzy [ u�c d 2 MOL(M'2 MlH�FJB %�. C+I(B�QWB<C+I(NPFJB�k?F?H�kJw ~+H<H�F?H��PC+Lk?C/2L2 FJLmk?F5A ~EB0I(LmF A ~EBWQWMOQWMlC+L 2 MOL(M'2 ~EwlFoK(F?H.RJQ�~EQ<H , wlF?H.RJQ�~EQ<H�\mL ~EI54 K y I(L k �+Q<R FJQ.wlF?H0LmC+L5� \mL ~EI54K(F;wzy ~EI(QWB<F % � k : ~/_ ImF.MOQ<RJB�~EQWMlC+LM� wzy ~EwO{PC+BWMOQ@:�2 F3K MONqMlH<F;wlF?H%A ~EBWQWMlF?H K(F;w ~xA ~EBWQWMOQWMlC+L k?C+I(B�~EL Q<F d k : ~/_ ImFDGC+MlHL_ I y I(L'{fB<C+I(A F K y RJQ�~EQ<H K(F k?FJQWQ<F A ~EBWQWMlF LmF H�F k?C/2 A C+BWQ<F A ~+H k?C/2L2 F wlF?H ~EI(QWB<F?H RJQ�~EQ<H K(F w ~A ~EBWQWMlFoHWI(BvI(L C+I A(wOImHWMlFJI(B<HxH@AB2,( C+wlF?H3K y FJL QWB<R?F?H|FJL QWB�~ELmHWMOQ�~EL QxNPFJB<H.I(L#RJQ�~EQxK M0/ RJB<FJL QxK(F?Hx~EI(QWB<F?H %j y ~EI(Q<C/2 ~EQ<F C/((Q<FJL I F?HWQ 2 MOL(M'2 ~Ew ��k?F _ I(M F?H<QoK(R32 C+L QWB�~�((wlF A ~EB k?C+L QWB�~+K MlkJQWMlC+L % n M I(L ~EI(Q<C/2 ~EQ<F~ A ~EL QN2 C+MOLmH K y RJQ�~EQN_ ImF wzy [ u�c _ ImF LmC+ImHoNPFJLmC+LmH K(F k?C+LmH<QWBWI(MOB<F A C+I(Nf~EMOQoB<F?k?C+L(L ~FElQWB<F wlF�2��32 Fw ~EL({ ~E{PFR_ ImF k?F#K(FJBWL(MlFJB��0~EwlC+B<H C+L8K(FJN B�~EMOQ A C+I(NPC+MOB wzy C/((Q<FJL(MOB FJL D ImHWMlC+L(L ~EL Q k?FJBWQ�~EMOLmH RJQ�~EQ<H K(Fwzy ~EI(Q<C/2 ~EQ<F�C/((Q<FJL I % � B;k?FJQWQ<F3D ImHWMlC+L L y F?HWQ0A ~+H�A CfH�HWM'((wlF3A(I(MlH _ ImF3wlF?H;RJQ�~EQ<H0FJL _ ImF?HWQWMlC+L L y ~EI(B�~EMlFJL QA ~+H�wlF+2��32 F�k?C/2 A C+BWQ<F32 FJL Q0QWB�~ELmHWMOQ<C+MOB<F % �� j F Q@:mR?C+B 032 F K(Fp2 MOL(M'2 MlH�~EQWMlC+L'K(F?H5~EI(Q<C/2 ~EQ<F?H K y RJQ�~EQ<H=\mL(MlH B<FJLmK�A(B�~EQWMlkc~�((wlF w ~ k?C+LmH<QWBWImkJQWMlC+LK y I(L ~EI(Q<C/2 ~EQ<F K(RJQ<FJB@2 MOL(MlH<Q<F FJL A ~+H<H�~EL Q A ~EB I(L ~EI(Q<C/2 ~EQ<F LmC+L5� K(RJQ<FJB@2 MOL(MlHWQ<F'C/((Q<FJL I A ~EB w ~k?C+LmHWQWBWImkJQWMlC+L K(F)ab:mC/2 AmH<C+L % }�MlFJL�_ ImF�w ~xk?C+LmHWQWBWImkJQWMlC+L K(F;wzy [ u�c MOL Q<FJB@2 R?K M ~EMOB<FvA(I(MlH<H<F;K(C+L(LmFJB�I(L~EI(Q<C/2 ~EQ<F0K(F;QWB 0?H�{fB�~ELmK(F;Q�~EMOwOwlF�� H�~�2 MOL(M'2 MlH�~EQWMlC+L LmC+ImH�~+H<HWI(B<F�K(F;Q<C+I(Q<F?H�Dz~$�?C+LmH%K(F�QWB<C+I(NPFJB�wlF�A(wOImHA FJQWMOQ�~EI(Q<C/2 ~EQ<F|B<F?k?C+L(L ~EMlH<H�~EL Q0wlF3w ~EL({ ~E{PF % <�FJBWQ<F?H�� MOw DG~EImK B�~ DGC+I(BWL(MOB�I(L F>/ C+BWQ�A C+I(B wlF�2 MOL(M'2 MlH<FJB��2 ~EMlH;k?FJw ~ F?H<Q DG~EMOQ;I(LmFvDGC+MlH�A C+I(B;Q<C+I(Q<F?H %j F A FJQWMOQ H<k;:mR32 ~�HWI(MONf~EL Q B<R?HWI�2 F wlF?H k?C+LmHWQWBWImkJQWMlC+LmH�_ ImF LmC+ImH ~?NPC+LmH A(B<R?H<FJL Q<R?F?H Km~ELmH k?FJQWQ<F

H<F?kJQWMlC+L A FJB@2 FJQWQ�~EL QoK(F A ~+H<H<FJB5K y I(LmF Fh4 A(B<F?H<HWMlC+L�B<RJ{fI(wOM10JB<F d K(F?Ho~EI(Q<C/2 ~EQ<F?HoFJQ�NqMlk?F NPFJB<H�~H� A(I(MlHK y ~EI(Q<C/2 ~EQ<F?H�FJL QWB<F3FJI54 � H�~EI D wlF.A ~+H<H�~E{PF3~EI54 [ uHf H^~ELmH ε �zQWB�~ELmH<MOQWMlC+L�_ ImF0LmC+ImH�L y ~?NPC+LmH A ~+H Fh4 A(wOMy�kJMOQ<F32 FJL Q.A(B<R?H<FJL Q<R � ,

X r //ZZ

��55

5555

[ u�f ~cNPF?k|QWB�~ELmHWMOQWMlC+L ε

xxppppppppppp

**[ u�cBCD??

@GA2 MOL(M'2 MlH�~EQWMlC+L

EE��

[ uHf H�~ELmH�QWB�~ELmHWMOQWMlC+L εoo

�5% ]p^ MlH<FxFJL A(B�~EQWM1_ ImF|K(F?H0~EwO{PC+BWMOQ@:�2 F?H $`C

� I"�HIJ��I"�P�5M`I"�� nJI1GH� j� � �� A ~EBWQWMOB%K y I(L [ uHc _ ImFJwlk?C+L�_ ImF M = (Q,Σ, δ, q0, F ) �Pk?C+L QWBWI(MOB<F0I(L [ u�c M ′ Q<FJw�_ ImF L(M) =L(M ′) FJQ�Q<FJw�_ ImF M ′ H<C+MOQ wlF A(wOImH A FJQWMOQ [ u�c B<F?k?C+L(L ~EMlH<H�~EL Q L(M)

� k?FJwOI(M�_ I(Mmk?C+L QWMlFJL Q�wlFb2 C+MOLmHK y RJQ�~EQ<H �h%$&% H<C+MOQ Π I(LmF|A ~EBWQWMOQWMlC+L MOL(MOQWM ~EwlF�K(F Q k?C+L Q<FJL ~EL Q3K(FJI54 FJLmH<F32,((wlF?H�, F FJQ Q \ F

%�5% MOL(MOQWM ~EwOMlH<FJB Πn

d w ~oA ~EBWQWMOQWMlC+L N MlK(F %75% MP��QM �OG��Π 6= Πn

��I"��]�% k �QG�� k : ~/_ ImF�FJLmH<F32=((wlF|K y RJQ�~EQ<H G K(F Π

� ��I"�F�-5% A ~EBWQWMOQWMlC+L(LmFJB G FJL H<C+ImH � FJLmH<F32=((wlF?H0K(FxQ<FJwOwlF3Dz~$�?C+L _ ImF|K(FJI54 RJQ�~EQ<H e FJQ t K(F G H<C+MlFJL Q

Km~ELmH�wlF+2��32 F|H<C+ImH@� FJLmH<F32,((wlF H<HWM ∀a ∈ Σ wlF?H;RJQ�~EQ<H e FJQ t C+L Q.K(F?H;QWB�~ELmHWMOQWMlC+LmH.HWI(Ba NPFJB<H0K(F?H0RJQ�~EQ<H;K I 2��32 F|FJLmH<F32=((wlF�Km~ELmH Π

%65% B<F32 A(w ~+k?FJB G Km~ELmH Πn

A ~EB;Q<C+ImH�wlF?H0H<C+ImH � FJLmH<F32=((wlF?H.~EMOLmHWM DGC+B@2 R?H %ST�CB% MOL Q<FJB<k : ~EL({PFJB Π FJQ Πn

%S��

�5% <�C+LmHWQWBWI(MOB<F M ′ FJL A(B<FJL ~EL Q.k?C/2L2 F�RJQ�~EQ<H q′iwlF?H0FJLmH<F32=((wlF|K y RJQ�~EQ<H0K(F M kc~EwlkJI(wlR?H0Km~ELmH Π �

Km~ELmH0w ~ D C+LmkJQWMlC+L δ′ � MOw�A ~EI(B�~oI(LmFxQWB�~ELmHWMOQWMlC+L K(F q′iNPFJB<H q′j

H<HWM MOw Fh4 MlHWQ�~EMOQ0Km~ELmH δ I(LmFQWB�~ELmHWMOQWMlC+L K y I(L RJQ�~EQ qm ∈ q′iNPFJB<H�I(L RJQ�~EQ qn ∈ q′j

�(wzy RJQ�~EQ0MOL(MOQWM ~Ew K(F M ′ F?HWQ�wzy RJQ�~EQ q′0k?C+L Q<FJL ~EL Q q0FJQ;wlF?H;RJQ�~EQ<H \mL ~EI54 H<C+L Q0k?FJI54 C/((Q<FJL ImH0K(F|w ~5A ~EBWQWMOQWMlC+L K(F F

%W5% r0FJQWMOB<FJB0K(F M ′ Q<C+I(Q0RJQ�~EQ;LmC+L5�s~+k?k?FJA(Q�~EL Q�_ I(M L y ~ K(F3QWB�~ELmHWMOQWMlC+LmH�_ ImF3NPFJB<H;wOI(My� 2��32 F�C+I

Q<C+I(Q0RJQ�~EQ0MOL ~EQWQ<FJMO{fL ~�((wlF K(FJA(I(MlH�wzy RJQ�~EQ0MOL(MOQWM ~Ew %

�� 5%8- � ^ MOL(M'2 MlH^~EQWMlC+L K y I(L ~EI(Q<C/2 ~EQ<F�\mL(M�K(RJQ<FJB@2 MOL(MlHWQ<F %

� �� 7 � 6 4 4�= � � - @ � 13254 # 4�6�-0: � � �� @�� !�4�6

c ~ELmHxk?FJQWQ<F H�F?kJQWMlC+LM� LmC+ImH|~EwOwlC+LmH3NPC+MOB|HWImk?k?F?H<HWMONPF32 FJL Q|k?C/2L2 FJL Q�k?C+LmHWQWBWI(MOB<FoI(L [ u�f d A ~EBWQWMOBK y I(LmF Fh4 A(B<F?H<HWMlC+L�B<RJ{fI(wOM10JB<F {fB��+k?F d w ~ k?C+LmHWQWBWImkJQWMlC+L K(Fpab:mC/2 AmH<C+LM� A(I(MlH�k?C/2L2 FJL Q5QWB�~ELmH[DGC+B@2 FJBk?FJQ [ u�f FJL [ uHc FJQ.FJLmHWI(MOQ<F�wlF*2 MOL(M'2 MlH<FJB % f C+ImH;NPFJBWB<C+LmHvFJLmHWI(MOQ<F k?C/2L2 FJL Qxk?C+LmHWQWBWI(MOB<F|I(L [ u�cK MOB<F?kJQ<F32 FJL Q d A ~EBWQWMOB0K(Fxwzy Fh4 A(B<F?H<HWMlC+L B<RJ{fI(wOM10JB<F %

�� "!��#%$&�'��

<�C+LmHWMlK(RJB<C+LmHxwzy Fh4 A(B<F?H<HWMlC+L B<RJ{fI(wOM10JB<F)(;�&*,+.- � ��+�+ % j ~ A(B<F32 M10JB<F RJQ�~EA F � NPC+MOB �5% � � k?C+LmHWMlHWQ<F d K(Rh�k?C/2 A CfH<FJB�wzy Fh4 A(B<F?H<HWMlC+L B<RJ{fI(wOM10JB<FvFJL H<F?H�H<C+ImH � Fh4 A(B<F?H<HWMlC+LmH�K(F)2 ~EL(M10JB<F d ~EA(A(wOM1_ ImFJB w ~|k?C+LmH<QWBWImkJQWMlC+LK(F�ab:mC/2 AmH�C+L A ~EB�MOLmK ImkJQWMlC+L HWI(B%w ~�HWQWBWImkJQWI(B<F.K(F0wzy Fh4qA(B<F?H�HWMlC+L % c ~ELmH�wlF0kc~+H�K(F;wzy Fh4 A(B<F?H<HWMlC+L A(B<R?k?Rh�K(FJL Q<F�� NPC+MlkJM�wzy ~EB@( C+B<F?H<k?FJLmk?F _ ImF|LmC+ImHvC/((Q<FJLmC+LmH � wlF?H.RJQWM1_ ImFJQWQ<F?H � $�� FJQ � 7 � LmC+ImH3H<FJBWNqMOB<C+L Q3K(FB<RiDGRJB<FJLmk?FxA ~EB;w ~oHWI(MOQ<F � ,

$ � j ~EL({ ~E{PF?H.B<RJ{fI(wOMlFJB<H0FJQ0~EI(Q<C/2 ~EQ<F?H�\mL(MlH� $��

// '&%$ !"#•??

?}}

}� � �// '&%$ !"#•

???

}}}}

/.-,()*++� 7 �

// '&%$ !"#•BB

BB||

||/.-,()*++

'&%$ !"#� '&%$ !"#�/.-,()*+*

@@@@

��'&%$ !"#� /.-,()*++

j ~ k?C+LmHWQWBWImkJQWMlC+L H<F DG~EMOQ5A ~EBoMOLmK ImkJQWMlC+L HWI(B w ~ HWQWBWImkJQWI(B<F K(F wzy Fh4qA(B<F?H�HWMlC+L B<RJ{fI(wOM10JB<F % <�C+LmHWMlK(Rh�B<C+LmHoK y ~�( C+B<K w ~ H<C+ImH � Fh4 A(B<F?H<HWMlC+Lo� w ~ A(wOImH d { ~EImk;:mF � FJL�( ~+H5K(F wzy ~EB@((B<F �h%�. ~EBow ~ B 0J{fwlF � K(F w ~k?C+LmHWQWBWImkJQWMlC+L K(F+ab:mC/2 AmH<C+LM� C+L C/((QWMlFJL Q�,

///.-,()*+2a // ?>=<89:;765401233

c F)2��32 F��PA C+I(B�w ~xH<C+ImH � Fh4 A(B<F?H<HWMlC+L +��[ImHWQ<F d K B<C+MOQ<F.K(F�w ~xA(B<R?k?R?K(FJL Q<F�� C+L C/((QWMlFJL Q�A ~EB%w ~�2��32 FB 0J{fwlF�,

///.-,()*+2b // ?>=<89:;765401233

j ~vH<C+ImH � Fh4 A(B<F?H<HWMlC+LoK y ~EwOQ<FJBWL ~EQWMONPF A(B<FJL ~EL Q wlF?H K(FJI54 H<C+ImH � Fh4 A(B<F?H<HWMlC+LmH)A(B<R?k?R?K(FJL Q<F?H%FJLo~EBW{fI�2 FJL QK(C+L(LmFxwOMlFJI d w ~ k?C+LmHWQWBWImkJQWMlC+L HWI(MONf~EL Q<F|A ~EB�w ~oB 0J{fwlF 7 ~ ,

/.-,()*+2a ///.-,()*+3

ε

&&MMMMMM

///.-,()*+1

ε99ssssss

ε

%%KKKKKK ?>=<89:;765401236

/.-,()*+4b ///.-,()*+5

ε 88qqqqqq

^ ~EMOL Q<FJL ~EL Q�� MOw DG~EI(Q0~EA(A(wOM1_ ImFJB;wzy C+A RJB�~EQ<FJI(B.K y MOQ<RJB�~EQWMlC+L y � y(HWI(B�wzy Fh4 A(B<F?H<HWMlC+L A(B<R?k?R?K(FJL Q<F %�. ~EB0w ~B 0J{fwlF 7 k�� C+L�K(C+MOQ5~F�[C+I(Q<FJB|I(L RJQ�~EQ|MOL(MOQWM ~Ew Z FJQxI(L�RJQ�~EQ*\mL ~Ew CB% t LmF ε �zQWB�~ELmHWMOQWMlC+L�B<FJwOMlF wzy RJQ�~EQ Z dwzy RJQ�~EQ $ A C+I(B;B<F?k?C+L(L ~FElQWB<F wzy Fh4 A(B<F?H<HWMlC+L A(B<R?k?R?K(FJL Q<F�I(LmF|D C+MlH0C+I A(wOImH % t LmF ε �zQWB�~ELmH<MOQWMlC+L B<FJwOMlF ~EImH�HWMwzy RJQ�~EQ Z d wzy RJQ�~EQ�\mL ~Ew C A C+I(B�LmF�B<F?k?C+L(L ~FElQWB<F)_ ImF w ~vk : ~FElLmF�NqMlK(F % t LmF;~EI(QWB<F ε �zQWB�~ELmH<MOQWMlC+L B<FJwOMlF wzy RJQ�~EQ6 d wzy RJQ�~EQ C A C+I(B>\mL(MOB w ~|B<F?k?C+L(L ~EMlH<H^~ELmk?F|~EA(B 0?H�I(LmFvC+I A(wOImHWMlFJI(B<H�B<F?k?C+L(L ~EMlH<H�~ELmk?F?H�K(F.wzy Fh4qA(B<F?H�HWMlC+LA(B<R?k?R?K(FJL Q<F %UX L5\mLM� I(LmF ε �zQWB�~ELmHWMOQWMlC+L�B<FJwOMlF wzy RJQ�~EQ 6 d wzy RJQ�~EQ $ A C+I(BxB<RJA RJQ<FJB|w ~ B<F?k?C+L(L ~EMlH<H�~ELmk?F K(Fwzy Fh4 A(B<F?H<HWMlC+L A(B<R?k?R?K(FJL Q<F ~EI(Q�~EL QvK(FvD C+MlH�_ ImF3wzy C+L NPFJI(Q % <�F?kJM K(C+L(LmFxwzy [ uHf ,

/.-,()*+2a ///.-,()*+3

ε

%%KKKKKK

///.-,()*+0ε //

@A BCε

OO

/.-,()*+1

ε99ssssss

ε

%%KKKKKK /.-,()*+6ε //

EDGFε

�� ?>=<89:;765401237

/.-,()*+4b ///.-,()*+5

ε99ssssss

X L ~EA(A(wOM1_ I ~EL Q d LmC+I(NPFc~EI w ~oB 0J{fwlF � HWI(B;w ~ H<C+ImH � Fh4 A(B<F?H<HWMlC+L � HWI(MON+~EL Q0M'2L2 R?K M ~EQ<F32 FJL Qvwzy C+A Rh�B�~EQ<FJI(B0K(F3DGFJB@2 FJQWI(B<F��mC+L QWB<C+I(NPF d LmC+I(NPFc~EI I(L A FJQWMOQ [ u�f k?C/2L2 FxwlF?H�A(B<R?k?R?K(FJL Q<H�,

//765401237′a // ?>=<89:;765401238

^ ~EMOL Q<FJL ~EL Q��MOw DG~EI(Q|Hcy ~EQWQ�~/_ ImFJB d wzy C+A RJB�~EQ<FJI(B�K(F k?C+Lmkc~EQ<RJL ~EQWMlC+L RJQWM1_ ImFJQ<R � 7 � Km~ELmH�wzy ~EB@((B<F FJQ_ I(M B<FJwOMlF5wlF?H.K(FJI54 H�C+ImH � Fh4qA(B<F?H�HWMlC+LmHvA(B<R?k?R?K(FJL Q<F?H % � L#~EA(A(wOM1_ ImFo~EwlC+B<Hvw ~ B 0J{fwlF 7 ( FJL HWI(A FJBWA CfH�~EL QwlF?H�RJQ�~EQ<H C FJQ C yqK(F?H�K(FJI54 A(B<R?k?R?K(FJL Q<H [ u�f FJQ�FJL DG~EMlH�~EL Q�K(F.wzy RJQ�~EQ � wzy RJQ�~EQ>\mL ~Ew K I LmC+I(NPFJw [ u�f ,

�5% ]p^ MlH<FxFJL A(B�~EQWM1_ ImF|K(F?H0~EwO{PC+BWMOQ@:�2 F?H $PW

/.-,()*+2a ///.-,()*+3

ε

%%KKKKKK

///.-,()*+0ε //

@A BCε

OO/.-,()*+1

ε99ssssss

ε

%%KKKKKK /.-,()*+6ε //

EDGFε

�� /.-,()*+7a // ?>=<89:;765401238

/.-,()*+4b ///.-,()*+5

ε99ssssss

� L B<RJAt0JQ<F.FJLmH<I(MOQ<F0K(F?H C+A RJB�~EQWMlC+LmH HWM'2 MOw ~EMOB<F?H�A C+I(B%QWB�~EMOQ<FJB�wlF?H�K(FJI54 K(FJBWL(M10JB<F?H�H�C+ImH � Fh4qA(B<F?H�HWMlC+LmH+ FJQ wlFJI(B<H�k?C+Lmkc~EQ<RJL ~EQWMlC+LmH�HWImk?k?F?H<H<MONPF?H d wzy ~EI(Q<C/2 ~EQ<F�B<R?HWI(wOQ�~EL Q�� k?F _ I(M LmC+ImH�K(C+L(LmF�k?C/2L2 F;B<R?HWI(wOQ�~EQ\mL ~Ew wzy [ u�f HWI(MONf~EL Q�,

/.-,()*+2a ///.-,()*+3

ε

%%KKKKKK

///.-,()*+0ε //

@A BCε

OO/.-,()*+1

ε99ssssss

ε

%%KKKKKK /.-,()*+6ε //

EDGFε

�� /.-,()*+7a ///.-,()*+8

b ///.-,()*+9b // GFED@ABC?>=<89:;10

/.-,()*+4b ///.-,()*+5

ε99ssssss

�� &�� $ �� &��

j y ~EwO{PC+BWMOQ@:�2 F|K(F3k?C+LmHWQWBWImkJQWMlC+L K y I(L [ u�c d A ~EBWQWMOB;K y I(L [ u�f � NPC+MOB �5% ] � k?C+LmH<MlHWQ<F d H<M'2�I(wlFJB;FJLA ~EB�~EwOw10JwlF Q<C+I(Q<F?H;wlF?H;QWB�~ELmH<MOQWMlC+LmH0A CfH<HWM'((wlF?H d A ~EBWQWMOB.K y I(L k?FJBWQ�~EMOL RJQ�~EQ.H<I(B;I(L H@AB2,( C+wlF�K y ~EwOA�: ~�( FJQK(C+L(LmR % psw Dz~EI(Q�RJ{ ~EwlF32 FJL Q�B<FJ{fB<C+I(A FJB�FJLoI(LoRJQ�~EQ Q<C+ImH wlF?H�RJQ�~EQ<H�~+k?k?F?H<H<M'((wlF?H A ~EB ε �zQWB�~ELmHWMOQWMlC+L d A ~EBWQWMOBK(F k;: ~+kJI(L'K(F?H RJQ�~EQ<H5k?C+LmHWQWBWI(MOQ<H��)K y C$;�wzy I(QWMOwOMlH�~EQWMlC+L'K y I(LmF A(B<C k?R?K I(B<F K y ε �GDGFJB@2 FJQWI(B<F�_ I(M�k?C+LmH<MlHWQ<FQ<C+I(Q3HWM'2 A(wlF32 FJL Q d QWB<C+I(NPFJB3A C+I(B0I(L FJLmH<F32,((wlF5K y RJQ�~EQ<H3K y I(L [ u�f Q<C+ImH0wlF?HvRJQ�~EQ<Hx~+k?k?F?H<HWM'((wlF?H.A ~EBε �zQWB�~ELmHWMOQWMlC+LmH %

<�C+LmHWMlK(RJB<C+LmH�wzy [ u�f C/((Q<FJL I d w ~ H<F?kJQWMlC+L A(B<R?k?R?K(FJL Q<F A C+I(B�wzy Fh4qA(B<F?H<H<MlC+L�B<RJ{fI(wOM10JB<F ( �* + - � � + +FJQ;K(RJB<C+I(wlC+LmH.wlF?H;RJQ�~EA F?H0K(Fxwzy MOQ<RJB�~EQWMlC+L K(F3w ~oA(B<Cqk?R?K I(B<F|K(Fxk?C+LmHWQWBWImkJQWMlC+L K(Fxwzy [ uHc %

� MP��k ��c � Q�~EQ<H ← {ε �GD FJB@2 FJQWI(B<F ({0})}< ~EwlkJI(wlC+LmH3~EI wlC+L({ k?FJQWQ<F ε �GD FJB@2 FJQWI(B<F % p L(MOQWM ~EwlF32 FJL Q.w ~oA(MOwlF�k?C+L QWMlFJL Qvwzy RJQ�~EQ Z �mLmC+Q<C+LmH0k?FJw ~ A(MOwlF ← Z��% j F|B<R?HWI(wOQ�~EQ<H3k?C+I(B�~EL Q3F?H<Q49 Z ; % � w ~ A(B<F32 M10JB<F5MOQ<RJB�~EQWMlC+LM� C+L k?C+LmHWMlK(RJB<F wzy RJQ�~EQ Z FJL H<C/2L2 FJQ3K(FA(MOwlF % j F?H�RJQ�~EQ<H ~+k?k?F?H�HWM'((wlF?H|A ~EB ε �zQWB�~ELmHWMOQWMlC+L d A ~EBWQWMOB K(F Z H�C+L Q $ FJQ CB% � L�wlF?H F32 A(MOwlF FJQ�C+L�wlF?H~F�WC+I(Q<F�~EI B<R?HWI(wOQ�~EQ��mk?F*_ I(M LmC+ImH0K(C+L(LmF|A(MOwlF ← $ � C�� FJQ;B<R?HWI(wOQ�~EQ ← 9 Z � $ � C ; %� w ~ H<F?k?C+LmK(FvMOQ<RJB�~EQWMlC+LM� C+L k?C+LmH<MlK�0JB<F.wzy RJQ�~EQ C _ I(M ~EA(A ~EB�~FElQ�FJL H�C/2L2 FJQ K(F.A(MOwlF �(~EImkJI(L RJQ�~EQ RJQ�~EL Q~+k?k?F?H<HWM'((wlF A ~EB ε �zQWB�~ELmHWMOQWMlC+L d A ~EBWQWMOB K(F C � w ~ A(MOwlF LmF k?C+L QWMlFJL Q A(wOImHN_ ImF wzy RJQ�~EQ $ FJQ wlF B<R?H<I(wOQ�~EQK(F32 FJI(B<F|MOLmk;: ~EL({PR %� w ~xQWB<C+MlH<M1032 F0MOQ<RJB�~EQWMlC+LM� C+L k?C+LmHWMlK�0JB<F0wzy RJQ�~EQ $&% j F?H�RJQ�~EQ<H�~+k?k?F?H<HWM'((wlF?H�A ~EB ε �zQWB�~ELmHWMOQWMlC+L d A ~EBWQWMOB K(F$ H<C+L Q � FJQ ]�% � L wlF?H0F32 A(MOwlF�FJQ;C+L wlF?H.~F�WC+I(Q<F�~EI B<R?HWI(wOQ�~EQ��mk?F,_ I(M K(C+L(LmF|A(MOwlF ← � � ]�� FJQ;B<R?H<I(wOQ�~EQ← 9 Z � $ � � � ] � C ; %� w ~L_ I ~EQWBWM1032 F|MOQ<RJB�~EQWMlC+LM� C+L k?C+LmHWMlK�0JB<F wzy RJQ�~EQ ] � ~EImkJI(L RJQ�~EQ.RJQ�~EL Q3~+k?k?F?H<HWM'((wlF�A ~EB ε �zQWB�~ELmHWMOQWMlC+L dA ~EBWQWMOB0K(F ] � w ~ A(MOwlF3LmF|k?C+L QWMlFJL Q0A(wOImH�_ ImF3wzy RJQ�~EQ � FJQ;wlF3B<R?H<I(wOQ�~EQ0K(F32 FJI(B<F|MOLmk;: ~EL({PR %� w ~ kJMOL�_ I(M1032 F|MOQ<RJB�~EQWMlC+LM� C+L k?C+LmHWMlK�0JB<F wzy RJQ�~EQ � � ~EImkJI(L RJQ�~EQ.RJQ�~EL Q3~+k?k?F?H<HWM'((wlF�A ~EB ε �zQWB�~ELmHWMOQWMlC+L dA ~EBWQWMOB0K(F � � w ~ A(MOwlFxK(FJN MlFJL Q0NqMlK(FxFJQ;wlF3B<R?HWI(wOQ�~EQ0K(F32 FJI(B<F�MOLmk : ~EL({PR %

�&Z j ~EL({ ~E{PF?H.B<RJ{fI(wOMlFJB<H0FJQ0~EI(Q<C/2 ~EQ<F?H�\mL(MlH

j y ~EwO{PC+BWMOQ@:�2 F K y ε �GD FJB@2 FJQWI(B<F Hcy ~EBWBP�JQ<F ~EwlC+B<HxA(I(MlH _ ImF5w ~ A(MOwlF F?HWQ3N MlK(F % j y RJQ�~EQ�MOL(MOQWM ~Ew�K(Fowzy [ u�c F?HWQK(C+Lmk|k?C+LmHWQWBWI(MOQ.k?C/2L2 Fxwzy FJLmH<F32,((wlF K y RJQ�~EQ<H 9 Z � $ � � � ] � C ;oK(Fxwzy [ u�f %

� MP��k � Dc � Q�~EQ<H ← {{0, 1, 2, 4, 7}}j F H<FJI(w RJQ�~EQo~+kJQWImFJwOwlF32 FJL Q Km~ELmH5wzy FJLmH<F32,((wlF K y RJQ�~EQ<H c � Q�~EQ<H F?HWQoH<RJwlF?kJQWMlC+L(LmR FJQoC+L Fh4m~�2 MOLmF H<F?HQWB�~ELmHWMOQWMlC+LmH3A CfH<HWM'((wlF?H3A C+I(Bvk?C+LmH<QWBWI(MOB<Fow ~ DGC+LmkJQWMlC+L�K(F5QWB�~ELmHWMOQWMlC+L#K(F5wzy [ u�c ~EA(A FJwlR?F c a B�~ELmH % p kJM �MOw Fh4 MlHWQ<FxI(L(M1_ ImF32 FJL Q.K(FJI54 H@AB2,( C+wlF?H;K y FJL QWB<R?F=,�� FJQ + %

DTrans[{0, 1, 2, 4, 7}, � ] = ε �GDGFJB@2 FJQWI(B<F (NTrans[0, � ] ∪NTrans[1, � ] ∪NTrans[2, � ] ∪NTrans[4, � ] ∪NTrans[7, � ])

= ε �GD FJB@2 FJQWI(B<F ({} ∪ {} ∪ {3} ∪ {} ∪ {8})= ε �GD FJB@2 FJQWI(B<F ({3, 8})= {1, 2, 3, 4, 6, 7, 8}

<�FJQ�RJQ�~EQ�L y Fh4 MlHWQ�~EL Q�A ~+H�FJLmk?C+B<F�� C+L wlF.B�~F�[C+I(Q<F d=c � Q�~EQ<H % <�C+LmHWMlK(RJB<C+LmH�FJLmHWI(MOQ<FvwlF?H�QWB�~ELmHWMOQWMlC+LmH�HWI(B+ ,

DTrans[{0, 1, 2, 4, 7}, + ] = ε �GDGFJB@2 FJQWI(B<F (NTrans[0, + ] ∪NTrans[1, + ] ∪NTrans[2, + ] ∪NTrans[4, + ] ∪NTrans[7, + ])

= ε �GD FJB@2 FJQWI(B<F ({} ∪ {} ∪ {} ∪ {5} ∪ {})= ε �GD FJB@2 FJQWI(B<F ({5})= {1, 2, 4, 5, 6, 7}

<�FJQ0RJQ�~EQ;L y Fh4 MlHWQ�~EL Q;A ~+H�LmC+L A(wOImH��(C+L wlF3B�~F�[C+I(Q<F dNc � Q�~EQ<H %

� MP��k � ic � Q�~EQ<H ← {{0, 1, 2, 4, 7}, {1, 2, 3, 4, 6, 7, 8}, {1, 2, 4, 5, 6, 7}}� L H<RJwlF?kJQWMlC+L(LmF|wzy RJQ�~EQ 9 $ � � � 7 � ] � 6 � C � � ; % j F?H;QWB�~ELmHWMOQWMlC+LmH.HWI(B � H<C+L Q!,

DTrans[{1, 2, 3, 4, 6, 7, 8}, � ] = ε �GDGFJB@2 FJQWI(B<F ({} ∪ {3} ∪ {} ∪ {} ∪ {} ∪ {8} ∪ {})= ε �GD FJB@2 FJQWI(B<F ({3, 8})= {1, 2, 3, 4, 6, 7, 8}

<�FJQ0RJQ�~EQ0Fh4 MlHWQ�~EL Q0K(R � d �(C+L L y ~5A ~+H d wlF3B�~F�WC+I(Q<FJB dLc � Q�~EQ<H % <�C+LmH<MlK(RJB<C+LmH;wlF?H�QWB�~ELmHWMOQWMlC+LmH.HWI(B + ,DTrans[{1, 2, 3, 4, 6, 7, 8}, + ] = ε �GDGFJB@2 FJQWI(B<F ({} ∪ {} ∪ {} ∪ {5} ∪ {} ∪ {} ∪ {9})

= ε �GD FJB@2 FJQWI(B<F ({5, 9})= {1, 2, 4, 5, 6, 7, 9}

<�FJQ0RJQ�~EQ;L y Fh4 MlHWQ�~EL Q;A ~+H;K(R � d �mC+L wlFxB�~F�WC+I(Q<F d c � Q�~EQ<H %

�5% ]p^ MlH<FxFJL A(B�~EQWM1_ ImF|K(F?H0~EwO{PC+BWMOQ@:�2 F?H �5$

� MP��k � �

c � Q�~EQ<H ← {{0, 1, 2, 4, 7}, {1, 2, 3, 4, 6, 7, 8}, {1, 2, 4, 5, 6, 7}, {1, 2, 4, 5, 6, 7, 9}}� L H<RJwlF?kJQWMlC+L(LmF|wzy RJQ�~EQ 9 $ � � � ] � - � 6 � C ;oFJQ;C+L Fh4(~�2 MOLmF|H�F?H QWB�~ELmHWMOQWMlC+LmH!,

DTrans[{1, 2, 4, 5, 6, 7}, � ] = ε �GD FJB@2 FJQWI(B<F ({} ∪ {3} ∪ {} ∪ {} ∪ {} ∪ {8})= ε �GDGFJB@2 FJQWI(B<F ({3, 8})= {1, 2, 3, 4, 6, 7, 8}

<�FJQ0RJQ�~EQ0Fh4 MlHWQ�~EL Q0K(R � d �(C+L L y ~5A ~+H d wlF3B�~F�WC+I(Q<FJB dLc � Q�~EQ<H % <�C+LmH<MlK(RJB<C+LmH;wlF?H�QWB�~ELmHWMOQWMlC+LmH.HWI(B + ,DTrans[{1, 2, 4, 5, 6, 7}, + ] = ε �GDGFJB@2 FJQWI(B<F ({} ∪ {} ∪ {5} ∪ {} ∪ {} ∪ {})

= ε �GD FJB@2 FJQWI(B<F ({5})= {1, 2, 4, 5, 6, 7}

<�FJQ0RJQ�~EQ0Fh4 MlHWQ�~EL Q0K(R � d �(C+L L y ~5A ~+H d wlF3B�~F�WC+I(Q<FJB dLc � Q�~EQ<H %

� MP��k � �

c � Q�~EQ<H ← {{0, 1, 2, 4, 7}, {1, 2, 3, 4, 6, 7, 8}, {1, 2, 4, 5, 6, 7}, {1, 2, 4, 5, 6, 7, 9}}� L H<RJwlF?kJQWMlC+L(LmF|wzy RJQ�~EQ 9 $ � � � ] � - � 6 � C � W ; % nqF?H;QWB�~ELmHWMOQWMlC+LmH0HWI(B � H<C+L Q:,

DTrans[{1, 2, 4, 5, 6, 7, 9}, � ] = ε �GDGFJB@2 FJQWI(B<F ({} ∪ {3} ∪ {} ∪ {} ∪ {} ∪ {8} ∪ {})= ε �GD FJB@2 FJQWI(B<F ({3, 8})= {1, 2, 3, 4, 6, 7, 8}

<�FJQ0RJQ�~EQ0Fh4 MlHWQ�~EL Q0K(R � d �(C+L L y ~5A ~+H d wlF3B�~F�WC+I(Q<FJB dLc � Q�~EQ<H % <�C+LmH<MlK(RJB<C+LmH;wlF?H�QWB�~ELmHWMOQWMlC+LmH.HWI(B + ,DTrans[{1, 2, 4, 5, 6, 7, 9}, + ] = ε �GDGFJB@2 FJQWI(B<F ({} ∪ {} ∪ {5} ∪ {} ∪ {} ∪ {} ∪ {10})

= ε �GDGFJB@2 FJQWI(B<F ({5, 10})= {1, 2, 4, 5, 6, 7, 10}

<�FJQ0RJQ�~EQ;L y Fh4 MlHWQ�~EL Q;A ~+H;K(R � d �mC+L wlFxB�~F�WC+I(Q<F d c � Q�~EQ<H %

� MP��k � #

c � Q�~EQ<H ← {{0, 1, 2, 4, 7}, {1, 2, 3, 4, 6, 7, 8}, {1, 2, 4, 5, 6, 7}, {1, 2, 4, 5, 6, 7, 9}, {1, 2, 4, 5, 6, 7, 10}}� L H<RJwlF?kJQWMlC+L(LmF|wzy RJQ�~EQ 9 $ � � � ] � - � 6 � C � $PZ ; % nqF?H;QWB�~ELmHWMOQWMlC+LmH0HWI(B�� H<C+L Q!,

DTrans[{1, 2, 4, 5, 6, 7, 10}, � ] = ε �GDGFJB@2 FJQWI(B<F ({} ∪ {3} ∪ {} ∪ {} ∪ {} ∪ {8} ∪ {})= ε �GDGFJB@2 FJQWI(B<F ({3, 8})= {1, 2, 3, 4, 6, 7, 8}

� � j ~EL({ ~E{PF?H.B<RJ{fI(wOMlFJB<H0FJQ0~EI(Q<C/2 ~EQ<F?H�\mL(MlH

<�FJQ0RJQ�~EQ0Fh4 MlHWQ�~EL Q0K(R � d �(C+L L y ~5A ~+H d wlF3B�~F�WC+I(Q<FJB dLc � Q�~EQ<H % <�C+LmH<MlK(RJB<C+LmH;wlF?H�QWB�~ELmHWMOQWMlC+LmH.HWI(B + ,DTrans[{1, 2, 4, 5, 6, 7, 10}, + ] = ε �GD FJB@2 FJQWI(B<F ({} ∪ {} ∪ {5} ∪ {} ∪ {} ∪ {} ∪ {})

= ε �GD FJB@2 FJQWI(B<F ({5})= {1, 2, 4, 5, 6, 7}

<�FJQ RJQ�~EQ Fh4 MlHWQ<F#K(R � d ~EImH<HWM ��FJQ K(C+Lmk c � Q�~EQ<H K(F32 FJI(B<F�MOLmk;: ~EL({PR % j F?H RJQ�~EQ<H K(F c � Q�~EQ<H RJQ�~EL Q2 ~EMOL Q<FJL ~EL Q Q<C+ImH 2 ~EB _ ImR?H��K(C+Lmk QWB�~EMOQ<R?H�� wzy ~EwO{PC+BWMOQ@:�2 F�Hcy ~EBWBP�JQ<F % n MxC+L�B<FJA(B<R?H<FJL Q<F#K(F 2 ~EL(M10JB<F{fB�~EA�:(M1_ ImFxwzy [ u�c B<R?HWI(wOQ�~EL Q�� C+L C/((QWMlFJL Q�,

/.-,()*+}a

�� b)) /.-,()*+c

aii

b��// /.-,()*+[

a ..

b// /.-,()*+<

a

HH

b

EE?>=<89:;76540123Xa

ZZ

b

ii

C$; [ 7 9 Z � $ � � � ] � C ;6�a} 7 9 $ � � � 7 � ] � 6 � C � � ;6�&<�7 9 $ � � � ] � - � 6 � C ;6� c 7 9 $ � � � ] � - � 6 � C � W ;6�EFJQ X 9 $ � � � ] � - � 6 � C � $PZ ; %

�� )�� $ �� $&��

j y ~EwO{PC+BWMOQ@:�2 F�K(F�k?C+LmHWQWBWImkJQWMlC+L K y I(L [ u�c d A ~EBWQWMOB)K(F�wzy Fh4 A(B<F?H<HWMlC+L|B<RJ{fI(wOM10JB<F � NPC+MOB �5%87 � F?H<Q�2 C+MOLmHRJNqMlK(FJL Q FJLmk?C+B<F _ ImF wlF A(B<R?k?R?K(FJL Q % j y MlK(R?F {PRJLmRJB�~EwlF F?HWQow ~ HWI(MON+~EL Q<F % � L'L I�2 RJB<C+Q<F wlF?HoA CfHWMOQWMlC+LmHKm~ELmH wzy Fh4 A(B<F?H<HWMlC+L B<RJ{fI(wOM10JB<FxC$; ~EA(A ~EB�~EMlH<H<FJL Q�wlF?H H@AB2,( C+wlF?H Q<FJB@2 MOL ~EI54 % j F?H RJQ�~EQ<H NPC+L Q;FJL _ ImFJw1_ ImFH<C+BWQ<F�B<FJA(B<R?H<FJL Q<FJBxK(F5FJLmH<F32,((wlF?H3K(F|A CfHWMOQWMlC+LmH3~EQWQ<FJMOL Q<F?HxK(FJA(I(MlH.wlF�K(R3((I(Q3K(F�w ~ B<F?k?C+L(L ~EMlH<H�~ELmk?FoK(Fw ~ k;: �EMOLmF��FJQ wlF?H|QWB�~ELmHWMOQWMlC+LmH NPC+L Q5H<FoDz~EMOB<F NPFJB<H|wlF?H�A CfH<MOQWMlC+LmH HWI(MONf~EL Q<F?H5~EQWQ<FJMOL Q<F?HoHWM�wlF A(B<C k;: ~EMOLH@AB2,( C+wlF|Km~ELmH�w ~ok;: ~FElLmF�F?HWQ�B<F?k?C+L(L I A ~EB;wzy I(LmF|K(F?H;A CfHWMOQWMlC+LmH0K(Fxwzy RJQ�~EQ0k?C+I(B�~EL QvK(Fxwzy ~EI(Q<C/2 ~EQ<F %j ~ DGC+LmkJQWMlC+L kc~EA(MOQ�~EwlF d C/((Q<FJL(MOB3F?HWQvK(C+Lmk�w ~ D C+LmkJQWMlC+L�� ' �� T �F2$@58S*L_ I(M � A C+I(Bvk : ~/_ ImF�A CfHWMOQWMlC+L

Km~ELmH|wzy Fh4 A(B<F?H<HWMlC+L B<RJ{fI(wOM10JB<F�� B<FJQ<C+I(BWLmF wlF?H|A CfHWMOQWMlC+LmH5HWI(MON+~EL Q<F?H,_ I(M�A FJI(NPFJL Q �JQWB<F ~EQWQ<FJMOL Q<F?H %�. C+I(Bkc~EwlkJI(wlFJB�k?FJQWQ<F�DGC+LmkJQWMlC+LM�fC+L A ~+H<H<F�A ~EB�QWB<C+MlH�~EI(QWB<F?H DGC+LmkJQWMlC+LmH ,�� @5@�� )W26%>)+*9�� P*># T�� (*�� ' .FJQ � * ��@5T � ��P*�� ' % <�F?H DGC+LmkJQWMlC+LmH%Hcy ~EA(A(wOM1_ ImFJL Q�HWI(B�wlF?H�L�3ImK(H�K(F�wzy ~EB@((B<F0K(F wzy Fh4qA(B<F?H<H<MlC+L B<RJ{fI(wOM10JB<F0FJQ�kc~EwlkJI(wlFJL QB<F?HWA F?kJQWMONPF32 FJL Q HWM�C+I(M�C+I LmC+L I(L L�3ImK A FJI(Q�B<F?k?C+L(L ~FElQWB<F w ~ H<C+ImH � k : ~FElLmF NqMlK(F�� wzy FJLmH�F32,((wlF K(F?HA(B<F32 M10JB<F?H�A CfH<MOQWMlC+LmH�~EI54�_ ImFJwOwlF?H C+L A FJI(Q�B<F?k?C+L(L ~FElQWB<FvwlF;A(B<Cqk : ~EMOL H@AB2,( C+wlF0Km~ELmH�w ~|k;: ~FElLmFvFJQ�wzy FJL5�H<F32=((wlF K(F?H K(FJBWL(M10JB<F?H A CfHWMOQWMlC+LmH ~EI545_ ImFJwOwlF?H C+L A FJI(Q B<F?k?C+L(L ~FElQWB<F wlF A(B<Cqk : ~EMOL H@AB2,( C+wlF Km~ELmH w ~k : ~FElLmF %

^ I(L(M;K(F?HoQWB<C+MlHoDGC+LmkJQWMlC+LmH � @�@ � )W26%>)+*9�� P*># T ��(*��' FJQ � * ��@5T � �P*�� '$ >��C+L kc~EwlkJI(wlF w ~ DGC+LmkJQWMlC+L� ' � �T �F2�@58S*9� d A ~EBWQWMOB�K(F w ~/_ ImFJwOwlF�C+L k?C+LmHWQWBWI(MOQ�wzy [ uHc % <�C+LmHWMlK(RJB<C+LmH�FJLmk?C+B<F�wzy Fh4qA(B<F?H�HWMlC+LoB<RJ{fI(wOM10JB<F(;�&*,+.- � ��+�+ A C+I(B�MOwOwOImHWQWB<FJB.k?FJQ.~EwO{PC+BWMOQ@:�2 F %

� ��!��IKr!�F� EmMP��k �N- ��GU��E��MP�5M`I"�� nU�!�Nk ��FI M`I"�Q��

� L�~F�[C+I(Q<F d wzy Fh4 A(B<F?H<HWMlC+L#B<RJ{fI(wOM10JB<F wlF5H A!2=( C+wlF y�� y�_ I(M�H<FJBWQ|K(F 2 ~EB _ ImFJI(B|K(F \mL�K(Fowzy Fh4 A(B<F?H �HWMlC+LM�qA(I(MlH�C+L k?C+LmHWQWBWI(MOQ wzy ~EB@((B<FxK(Fvwzy Fh4qA(B<F?H<H<MlC+L C$; C+L L I�2 RJB<C+Q<F3wlF?H A CfHWMOQWMlC+LmH k?C+BWB<F?HWA C+LmKm~EL Q.~EI54H@AB2,( C+wlF?H;K(Fxwzy ~EwOA�: ~�( FJQ0K y FJL QWB<R?F5~EI({&2 FJL Q<R K(F y�� y ,

�5% ]p^ MlH<FxFJL A(B�~EQWM1_ ImF|K(F?H0~EwO{PC+BWMOQ@:�2 F?H �&7

f �3ImK(H � @�@��)W26%>)+* � �(*># T�� P*�� ' � * ��@5T � �P*�� '$ � $�� DG~EI54 9 $ ; 9 $ ;� � � DG~EI54 9 � ; 9 � ;� 7 � DG~EI54 9 7 ; 9 7 ;� ] � DG~EI54 9 ] ; 9 ] ;� - � DG~EI54 9 - ; 9 - ;� 6 � DG~EI54 9 6 ; 9 6 ;/.-,()*+*

::��'&%$ !"#� /.-,()*++A� $�� C+I A

� $�� 7 DG~EI54 P� $��∪ P

� � � 7 9 $ � � ; D� $��∪ D

� � � 7 9 $ � � ;

'&%$ !"#�/.-,()*+*

NqB�~EM P� * � 7 9 $ � � ; D

� * � 7 9 $ � � ;

'&%$ !"#• @@~~'&%$ !"#� '&%$ !"#�DG~EI54 P

� � � 7 9 $ � � ; D� � � 7 9 7 ;

'&%$ !"#• ??��'&%$ !"#• /.-,()*++DG~EI54 P

�•� 7 9 $ � � ; D

� + � 7 9 ] ;

'&%$ !"#• ??��'&%$ !"#• /.-,()*++DG~EI54 P

�•� 7 9 $ � � ; D

� + � 7 9 - ;

'&%$ !"#• ??��'&%$ !"#• /.-,()*+�DG~EI54 P

�•� 7 9 $ � � ; D

� � � 7 9 6 ;

�� 5%86 � a)~�((wlFc~EI K(F?H|DGC+LmkJQWMlC+LmH � @�@��)02 %>)W* �� P*># T�� (*�� ' FJQ � * �>@�T�� (*�� ' A C+I(B wzy Fh4qA(B<F?H�HWMlC+LB<RJ{fI(wOM10JB<F ( �* + - � � + + %

'&%$ !"#•BB

BB||

||'&%$ !"#•AA

AA

}}}}

/.-,()*+�'&%$ !"#•

AAAA

}}}}

/.-,()*++ � 6 �'&%$ !"#•

BBBB

~~~

/.-,()*++ � - �'&%$ !"#� '&%$ !"#� � ] �/.-,()*+*

>>>

��

� 7 �'&%$ !"#� /.-,()*++� $��

�,�� "l�GH >nH��L� ��Ul&M`I"��U�� m� ��(��= (��)�#"�$ �mM%'�(�)��! ��#"�$� LxDG~�((BWM1_ ImF�I(L|Q�~�((wlFc~EI K(C+L Q wlF?H�FJL QWB<R?F?H�:mC+BWM �cC+L Q�~EwlF?H H<C+L Q wlF?H L�3ImK(H K(F�wzy ~EB@((B<F�K(F wzy Fh4qA(B<F?H�HWMlC+L

B<RJ{fI(wOM10JB<F FJQ wlF?H FJL QWB<R?F?H NPFJBWQWMlkc~EwlF?H H�C+L Q wlF?H QWB<C+MlH DGC+LmkJQWMlC+LmH % j F Q�~�((wlFc~EI C/((Q<FJL I8~EA(A ~EB�~FElQ d w ~\m{fI(B<F �5%865% � A ~EBWQWMOB3K(F5k?F?HvQWB<C+MlHvD C+LmkJQWMlC+LmH�� C+L#kc~EwlkJI(wlF5w ~ DGC+LmkJQWMlC+L � ' � � T �F2$@Q8S* % <�C+L QWB�~EMOB<F32 FJL Q~EI54�QWB<C+MlH�A(B<R?k?R?K(FJL Q<F?H��+w ~;DGC+LmkJQWMlC+L � '$ � �T � 2$@58S*�A(B<FJLmK5FJL5FJL QWB<R?F K(F?H A CfHWMOQWMlC+LmH��EFJQ�LmC+LoK(F?H�L�3ImK(H��FJQ0FJwOwlF�B<FJQ<C+I(BWLmF K(F?H.FJLmH<F32,((wlF?HvK(F|A CfHWMOQWMlC+LmH % psw HWIHG Q.K(C+Lmk�K(F|w ~ kc~EwlkJI(wlFJB.A C+I(B;wlF?H;A CfHWMOQWMlC+LmH $ d65%

. C+I(B.w ~oA CfH<MOQWMlC+L $ �mC+L k?C+LmHWQ�~EQ<F=_ ImF $ ~EA(A ~EB�~FElQ.Km~ELmH � * �>@�T�� (*�� ' � � � � K(C+LmkxA ~EB0w ~ B 0J{fwlF|K(F?HMOQ<RJB�~EQWMlC+LmHvC+L ~F�[C+I(Q<F#� �(*9# T�� P*�� ' � � �h%Q. ~EBv~EMOwOwlFJI(B<H��(wlFxL�3ImK K(F�k?C+Lmkc~EQ<RJL ~EQWMlC+L Hcy ~EA(A(wOM1_ I ~EL QvHWI(B

��] j ~EL({ ~E{PF?H.B<RJ{fI(wOMlFJB<H0FJQ0~EI(Q<C/2 ~EQ<F?H�\mL(MlH

wzy MOQ<RJB�~EQWMlC+L ~ $ Km~ELmH wlF?H�K(FJBWL(M10JB<F?H�A CfH<MOQWMlC+LmH)K(F H<C+LoL�3ImK K(F�{ ~EImk :mF��fK(C+Lmk�C+L ~F�WC+I(Q<F�wlF?H A(B<F32 M10JB<F?HA CfHWMOQWMlC+LmH;K(F|H<C+L L�3ImK K(F|K B<C+MOQ<F��mkfy F?HWQ � d � K MOB<F�� (*># T�� P*�� ' � � � 7 9 7 ; % � L C/((QWMlFJL Q.K(C+Lmk�,

PosSuivante(1) = {1, 2} ∪ {3} = {1, 2, 3}. C+I(B3w ~ A CfHWMOQWMlC+L � � C+L ~ Fh4m~+kJQ<F32 FJL Q3wlF,2��32 F5B�~EMlH<C+L(LmF32 FJL Q*_ ImF A C+I(B.w ~ A CfH<MOQWMlC+L $ � k?F=_ I(M

LmC+ImH;K(C+L(LmF=,PosSuivante(2) = {1, 2} ∪ {3} = {1, 2, 3}. C+I(B.w ~oA CfH<MOQWMlC+L 7 �mk?FJQWQ<F|A CfHWMOQWMlC+L ~EA(A ~EB�~FElQvKm~ELmH�wlF?H0K(FJBWL(M10JB<F?H.A CfHWMOQWMlC+LmH;K I L�3ImK K(F|k?C+Lmkc~F�

Q<RJL ~EQWMlC+L _ I(M ~5A C+I(B;L�3ImK K(FxK B<C+MOQ<FxwlF + FJL A CfH<MOQWMlC+L ]�% � L ~oK(C+Lmk�,PosSuivante(3) = {4}. C+I(B.wlF?H;A CfHWMOQWMlC+LmH ] FJQ - � FJLmk?C+B<F|I(LmF3DGC+MlH;FJwOwlF?H.~EA(A ~EB�~EMlH�H<FJL QvKm~ELmH;wlF?H;K(FJBWL(M10JB<F?H.A CfH<MOQWMlC+LmH0K I

L�3ImK K(F�{ ~EImk :mF�K y I(LoL�3ImK K(F k?C+Lmkc~EQ<RJL ~EQWMlC+L K(C+L Q�wlF?H)A(B<F32 M10JB<F?H�A CfHWMOQWMlC+LmH B<F?HWA F?kJQWMONPF?H�K IoL�3ImKK(F|K B<C+MOQ<F|H�C+L Q 9 - ;�FJQ 9 6 ;6� K y C$; ,

PosSuivante(4) = {5}

PosSuivante(5) = {6}. C+I(Bvw ~oA CfHWMOQWMlC+L 6 � ~EImkJI(LmF�B 0J{fwlF�Hcy ~EA(A(wOM1_ ImF �mwzy FJLmH�F32,((wlF5K(F�H<F?H�A CfHWMOQWMlC+LmH.HWI(MON+~EL Q<F?H.F?H<Q0K(C+Lmk

NqMlK(F %

�,��U� MP�/G�lmM`IK�Q�onH� I1j �t L A FJI d w ~�2 ~EL(M10JB<F.K(F;wzy ~EwO{PC+BWMOQ@:�2 F.K(F;k?C+LmHWQWBWImkJQWMlC+L K(F�wzy [ u�c d A ~EBWQWMOB�K(F�wzy [ u�f �fwlF�A(B<R?H<FJL Q

~EwO{PC+BWMOQ@:�2 Fok?C+LmHWQWBWI(MOQ3wzy [ u�c d A ~EBWQWMOB3K y I(L RJQ�~EQvMOL(MOQWM ~Ew�FJQvFJL Fh4(~�2 MOL ~EL Q3wlF?H0QWB�~ELmHWMOQWMlC+LmH d A ~EBWQWMOBK(Fxk : ~/_ ImF|RJQ�~EQ;k?C+LmHWQWBWI(MOQ % j y RJQ�~EQ;MOL(MOQWM ~Ew F?HWQ;C/((Q<FJL I A ~EB;wlF?H A(B<F32 M10JB<F?H0A CfHWMOQWMlC+LmH0K I L�3ImK B�~+kJMOLmFK(Fxwzy ~EB@((B<F|K(F3wzy Fh4 A(B<F?H<HWMlC+L B<RJ{fI(wOM10JB<F&,c � Q�~EQ<H57 {{1, 2, 3}}� �P*># T ��(*�TU8SR �(2�8UTU'�@� L H<RJwlF?kJQWMlC+L wzy RJQ�~EQ'9 $ � � � 7 ; A C+I(B kc~EwlkJI(wlFJB wlF?H RJQ�~EQ<H C/((Q<FJL I A ~EB QWB�~ELmHWMOQWMlC+L HWI(B k : ~+kJI(L K(F?H

H@AB2,( C+wlF?H K(F wzy ~EwOA�: ~�( FJQoK y FJL QWB<R?F Σ 7 9!~H� (�; %U. C+I(B H�~?NPC+MOB _ ImFJwOwlF?HoH<C+L Q wlF?H A CfHWMOQWMlC+LmH d ~F�WC+I(Q<FJBd wzy RJQ�~EQ3NPFJB<H3wlF _ ImFJw�C+L N+~H� MOw)DG~EI(Q3kJI�2�I(wlFJB�wlF?H.A CfHWMOQWMlC+LmHxHWI(MONf~EL Q<F?HxK(F5Q<C+I(Q<F?H3wlF?HvA CfHWMOQWMlC+LmHxKm~ELmHwzy RJQ�~EQ k?C+I(B�~EL QN_ I(M�k?C+BWB<F?HWA C+LmK(FJL Q ~EI'H@AB2,( C+wlF K y FJL QWB<R?F % . C+I(B wlF H@A!2=( C+wlF#y ~ yW�)wlF?HoA CfHWMOQWMlC+LmH K(Fwzy RJQ�~EQ0k?C+I(B�~EL Q.H<C+L Q $ FJQ 75% C+L ~oK(C+Lmk�,

c a B�~ELmH 9 $ � � � 7 ;6� ~ � 7 � ' �� T �F2$@58S* � $�� ∪ � '$ � �T � 2$@58S* � 7 � 7 9 $ � � � 7 ; ∪ 9 ] ; 7 9 $ � � � 7 � ] ;<�FJQ0RJQ�~EQ;L y Fh4 MlHWQ�~EL Q;A ~+H��(C+L wzy ~F�[C+I(Q<F d c � Q�~EQ<H %. C+I(B wlF H@A!2=( C+wlF y ( yW� w ~ H<FJI(wlFoA CfH<MOQWMlC+LR_ I(M�k?C+BWB<F?HWA C+LmK(F F?HWQ � � C+L#A(B<FJLmK�K(C+Lmk H<F?H3A CfHWMOQWMlC+LmH

HWI(MONf~EL Q<F?H�,c a B�~ELmH 9 $ � � � 7 ;6� ( � 7 � ' �� T �F2$@58S* � � � 7 9 $ � � � 7 ;<�FJQ0RJQ�~EQ0F?HWQ�wzy RJQ�~EQ0k?C+I(B�~EL Q�� K(C+Lmk|C+L LmF|wzy ~F�[C+I(Q<FxA ~+H dLc � Q�~EQ<H %

� *�� T �>#&*�TU8SR �(2�8UTU'�@c � Q�~EQ<H57 {{1, 2, 3}, {1, 2, 3, 4}}� L H<RJwlF?kJQWMlC+L(LmF wzy RJQ�~EQ49 $ � � � 7 � ] ;6� A ~EB@2 M wlF _ ImFJw wlF?H0A CfHWMOQWMlC+LmH.k?C+BWB<F?HWA C+LmKm~EL Q d I(L y ~ y H<C+L Q $ FJQ7 FJQ0k?FJwOwlF?H;k?C+BWB<F?H<A C+LmKm~EL Q d I(L�y ( ymH�C+L Q � FJQ ]�% � L ~oK(C+Lmk�,c a B�~ELmH 9 $ � � � 7 � ] ;6� ~ � 7 � ' � � T �F2$@Q8S* � $�� ∪ ��' � �T �F2$@58S* � 7 � 7 9 $ � � � 7 � ] ;

�5% ]p^ MlH<FxFJL A(B�~EQWM1_ ImF|K(F?H0~EwO{PC+BWMOQ@:�2 F?H �&-

c a B�~ELmH 9 $ � � � 7 � ] ;6� ( � 7 � ' � � T �F2$@Q8S* � � �∪ ��' � �T �F2$@58S* � ] � 7 9 $ � � � 7 ; ∪ 9 - ; 7 9 $ � � � 7 � - ;

<�F|K(FJBWL(MlFJB0RJQ�~EQ0F?HWQ0~F�WC+I(Q<R d c � Q�~EQ<H %> � '$T �T��>#&*:TA8SR �(2�8UT '$@c � Q�~EQ<H57 {{1, 2, 3}, {1, 2, 3, 4}, {1, 2, 3, 5}}� LoH�RJwlF?kJQWMlC+L(LmF wzy RJQ�~EQ 9 $ � � � 7 � - ;6�+A ~EB@2 M(wlF _ ImFJw wlF?H)A CfH<MOQWMlC+LmH�k?C+BWB<F?HWA C+LmKm~EL Q d I(L y ~ yEH�C+L Q�FJLmk?C+B<F$ FJQ 7 FJQ0k?FJwOwlF?H0k?C+BWB<F?HWA C+LmKm~EL Q d I(L�y ( y H<C+L Q � FJQ -5% � L ~oK(C+Lmk�,c a B�~ELmH 9 $ � � � 7 � - ;6� ~ � 7 � ' � � T �F2$@Q8S* � $�� ∪ ��' � �T �F2$@58S* � 7 � 7 9 $ � � � 7 � ] ;c a B�~ELmH 9 $ � � � 7 � - ;6� ( � 7 � ' � � T �F2$@Q8S* � � �

∪ ��' � �T �F2$@58S* � - � 7 9 $ � � � 7 ; ∪ 9 6 ; 7 9 $ � � � 7 � 6 ;<�F|K(FJBWL(MlFJB0RJQ�~EQ0F?HWQ0~F�WC+I(Q<R d c � Q�~EQ<H %

� �H2 8 ��T��>#&*!TA8SR �(2�8UT '$@c � Q�~EQ<H57 {{1, 2, 3}, {1, 2, 3, 4}, {1, 2, 3, 5}, {1, 2, 3, 6}}� LoH�RJwlF?kJQWMlC+L(LmF wzy RJQ�~EQ 9 $ � � � 7 � 6 ;6�+A ~EB@2 M(wlF _ ImFJw wlF?H)A CfH<MOQWMlC+LmH�k?C+BWB<F?HWA C+LmKm~EL Q d I(L y ~ yEH�C+L Q�FJLmk?C+B<F$ FJQ 7 FJQ0k?FJwOwlF�k?C+BWB<F?HWA C+LmKm~EL Q d I(L�y ( y(F?H<Q �5% � L ~ K(C+Lmk�,c a B�~ELmH 9 $ � � � 7 � 6 ;6� ~ � 7 � ' � � T �F2$@Q8S* � $�� ∪ ��' � �T �F2$@58S* � 7 � 7 9 $ � � � 7 � ] ;c a B�~ELmH 9 $ � � � 7 � 6 ;6� ( � 7 � ' � � T �F2$@Q8S* � � � 7 9 $ � � � 7 ;<�F?H RJQ�~EQ<H Fh4qMlHWQ<FJL Q K(R � d FJQ K(C+Lmk LmF H<C+L QoA ~+H ~F�WC+I(Q<R?H d c � Q�~EQ<H % a�C+ImH wlF?HoRJQ�~EQ<H K(F c � Q�~EQ<H

H<C+L Q=2 ~EMOL Q<FJL ~EL QN2 ~EB _ ImR?H��)k?F�_ I(M�Q<FJB@2 MOLmF wzy ~EwO{PC+BWMOQ@:�2 F % n M C+L LmC+Q<F�((MlFJL _ ImF wlF?H RJQ�~EQ<H=\mL ~EI54K(F wzy [ u�c H<C+L Qvk?FJI54 _ I(M k?C+L QWMlFJL(LmFJL Qxw ~ A CfHWMOQWMlC+L K I H@AB2,( C+wlF � ~F�WC+I(Q<R d wzy Fh4 A(B<F?H<HWMlC+L B<RJ{fI(wOM10JB<F��wzy ~EI(Q<C/2 ~EQ<F|B<R?H<I(wOQ�~EL Q.F?H<Q:,

/.-,()*+}a

��b

##// /.-,()*+[

a ..b

�� /.-,()*+<a

cc

bpp?>=<89:;76540123c

a

HH

b

bb

C$; [ 7 9 $ � � � 7 ;6�m} 7 9 $ � � � 7 � ] ;6�Q< 7:9 $ � � � 7 � - ;6�mFJQ c 7 9 $ � � � 7 � 6 ; %

�� # �� .��

j y ~EwO{PC+BWMOQ@:�2 F K(Fp2 MOL(M'2 MlH^~EQWMlC+L H�FN( ~+H<F HWI(B�wlF A(BWMOLmkJMOA F K(F B<FJ{fB<C+I(A F32 FJL Q FJL kJw ~+H<H�F?H K y R _ I(My�Nf~EwlFJLmk?F K(F?HvRJQ�~EQ<H.K(F wzy ~EI(Q<C/2 ~EQ<F5MOL(MOQWM ~EwH_ I(M�C+L Q.wlF,2��32 F k?C/2 A C+BWQ<F32 FJL Q %�^ �32 F5k?C/2 A C+BWQ<F32 FJL QKm~ELmH k?F kc~+H NPFJI(Q K MOB<F wlF?HL2��32 F?H QWB�~ELmHWMOQWMlC+LmH H<I(B wlF?H H@AB2,( C+wlF?H K y FJL QWB<R?F % j F A(BWMOLmkJMOA F {PRJLmRJB�~Ew~ K(R � d RJQ<R RJNPC!_ ImR % � L N+~ A ~EBWQWMOQWMlC+L(LmFJB wlF?HoRJQ�~EQ<H K(F wzy [ u�c K(F�2 ~EL(M10JB<F d k :mFJB<k :mFJB wlF?H5kJw ~+H�H<F?HK y R _ I(MON+~EwlFJLmk?F|K y RJQ�~EQ<H %

<�C+LmHWMlK(RJB<C+LmH0wzy ~EI(Q<C/2 ~EQ<F C/((Q<FJL I K(Fxwzy Fh4qA(B<F?H�HWMlC+L B<RJ{fI(wOM10JB<F ( �* + - � � + + A ~EB;w ~ k?C+LmH<QWBWImkJQWMlC+L K(Fab:mC/2 AmH<C+L A(I(MlH0QWB�~ELmH[DGC+B@2 ~EQWMlC+L FJL [ uHc ,

/.-,()*+}a

�� b)) /.-,()*+c

aii

b��// /.-,()*+[

a ..

b// /.-,()*+<

a

HH

b

EE?>=<89:;76540123Xa

ZZ

b

ii

j ~oA(B<F32 M10JB<F�RJQ�~EA F|K(RJQ<FJB@2 MOLmF�I(LmFxA ~EBWQWMOQWMlC+L 2 MOL(M'2 ~EwlF K(Fxwzy [ u�c ,mK y I(L k �+Q<R|wlF?H0RJQ�~EQ<Hb\mL ~EI54

�&6 j ~EL({ ~E{PF?H.B<RJ{fI(wOMlFJB<H0FJQ0~EI(Q<C/2 ~EQ<F?H�\mL(MlH

FJQ K(F wzy ~EI(QWB<F wlF?H LmC+L5� \mL ~EI54 % <vy F?HWQ FJL F>/ FJQ HWI(B wlF k?C/2 A C+BWQ<F32 FJL Q K y ~+k?k?FJA(Q�~EQWMlC+L C+I�K(F LmC+L5�~+k?k?FJA(Q�~EQWMlC+L _ ImF�wzy C+L K(C+MOQ�LmR?k?F?H<H�~EMOB<F32 FJL Q�K MlHWQWMOL({fImFJB�wlF?H%RJQ�~EQ<H %�. C+I(B�LmC+QWB<F.~EI(Q<C/2 ~EQ<F��qk?FJw ~xK(C+L(LmFk?C/2L2 FxA(B<F32 M10JB<F�A ~EBWQWMOQWMlC+L Π0

,Π0 = {Q\F, F} = {{A,B,C,D}, {E}}^ ~EMOL Q<FJL ~EL Q�� MOw�DG~EI(Q5NPRJBWMy\ FJB k : ~+kJI(L K(F?HoH<C+ImH � FJLmH<F32=((wlF?HoK y RJQ�~EQ<HoA C+I(B5NPC+MOB5H<M�Q<C+ImH5wlF?HoRJQ�~EQ<H

_ I(M ~EA(A ~EBWQWMlFJL(LmFJL Q d k?FvH<C+ImH � FJLmH<F32=((wlF3C+L Qb((MlFJL wlF 2��32 F3k?C/2 A C+BWQ<F32 FJL Q;HWI(B�wlFJI(B<H�QWB�~ELmH<MOQWMlC+LmH % pswHcy ~E{fMOQ�K(C+Lmk�K(F NPRJBWMy\ FJB�HWM(A C+I(B Q<C+ImH�wlF?H�RJQ�~EQ<H�K I H<C+ImH@� FJLmH<F32,((wlF;Hay MOwlH QWB�~ELmHWMOQ<FJL Q�Q<C+ImH�NPFJB<H�K(F?H�RJQ�~EQ<HK I 2��32 F H<C+ImH@� FJLmH<F32,((wlF K(F w ~ A ~EBWQWMOQWMlC+L�HWI(B|k : ~+kJI(L K(F?H|H@AB2,( C+wlF?HxK y FJL QWB<R?F % c ~ELmH|w ~ A ~EBWQWMOQWMlC+LA(B<R?k?R?K(FJL Q<F�� wlF?H|RJQ�~EQ<H [ � } FJQ=< QWB�~ELmH<MOQ<FJL Q|NPFJB<HxwlF 2��32 F H<C+ImH � FJLmH<F32=((wlF d w ~ D C+MlH3A C+I(B�~ FJQ+(M�2 ~EMlH�wzy RJQ�~EQ c �(H<I(B0~H� QWB�~ELmHWMOQ<FxwOI(M NPFJB<H�wzy RJQ�~EQ X ��_ I(M F?HWQ0Km~ELmH�wzy ~EI(QWB<F|H�C+ImH � FJLmH<F32,((wlF %� L N+~vK(C+Lmk�A ~+H<H<FJB d I(LmF�LmC+I(NPFJwOwlF�A ~EBWQWMOQWMlC+L C$; wzy RJQ�~EQ c F?HWQ�H<RJA ~EB<R�K IoA(B<F32 MlFJB�H<C+ImH � FJLmH<F32=((wlF %j y I(L K(F?H A C+MOL Q<H d NPRJBWMy\ FJB ~?NPF?k A(B<R?kc~EI(QWMlC+L wlC+B<H K(F k?FJQWQ<F RJQ�~EA F F?HWQ K(F kJB<R?FJB wlF 2 MOL(M'2�I�2 K(F

LmC+I(NPFc~EI54 H<C+ImH@� FJLmH<F32,((wlF?H %Q[ MOLmHWM �mMOw�DG~EI(Q 2 ~EMOL Q<FJL(MOBxKm~ELmHvwlF*2��32 F5H<C+ImH � FJLmH<F32=((wlF�Q<C+ImHvwlF?HvRJQ�~EQ<H_ I(M;C+L Q wlF 2��32 F k?C/2 A C+BWQ<F32 FJL Q N MlH � d �zNqMlH K(F w ~ A ~EBWQWMOQWMlC+L k?C+I(B�~EL Q<F % p kJM � LmC+ImH L y ~?NPC+LmH A ~+H k?FA(B<C/((w1032 F�FJQ;C+L C/((QWMlFJL Q0I(LmFxK(FJI54 M1032 F|A ~EBWQWMOQWMlC+LN,

Π1 = {{A,B,C}, {D}, {E}}� L B<FJA(B<FJLmK#~EwlC+B<H3I(LmF LmC+I(NPFJwOwlF A�: ~+H�F K(F5NPRJBWMy\ kc~EQWMlC+L % p kJM � [ FJQ*<�NPC+L Q3NPFJB<Hv} HWI(Bx~ FJQvNPFJB<H[ C+I < HWI(B�( �(MOwlH0C+L Q0K(C+Lmk|wlF+2��32 F k?C/2 A C+BWQ<F32 FJL Q %�. ~EB.k?C+L QWB<F�� } QWB�~ELmH<MOQ<F+((MlFJL NPFJB<H0wlF+2��32 F

H<C+ImH � FJLmH�F32,((wlF5HWI(B.~L2 ~EMlH.A ~+H0H<I(B�( C$; MOw QWB�~ELmHWMOQ<F�NPFJB<H c % � L K(C+MOQ.K(C+Lmk H<RJA ~EB<FJB.}8K I A(B<F32 MlFJBH<C+ImH � FJLmH�F32,((wlF�� k?F+_ I(M K(C+L(LmF|I(LmF3LmC+I(NPFJwOwlF�A ~EBWQWMOQWMlC+LN,

Π2 = {{A,C}, {B}, {D}, {E}}� k?FJQWQ<F;RJQ�~EA F��fFJL NPRJBWMy\ ~EL Q�� C+L H<F�B<FJLmK k?C/2 A(Q<F)_ ImF Q<C+ImH�wlF?H�RJQ�~EQ<H%C+L Q�wlF 2��32 F0k?C/2 A C+BWQ<F32 FJL Q

K(FvQWB�~ELmHWMOQWMlC+L % j ~5A ~EBWQWMOQWMlC+L B<R?HWMlH<Q<F d w ~ NPRJBWMy\ kc~EQWMlC+LM�mk?F�_ I(M ~EBWBP�JQ<Fvwzy ~EwO{PC+BWMOQ@:�2 F % j y [ u�c 2 MOL(M'2 ~EwC/((Q<FJL I8F?H<Q k?C+LmH<QWBWI(MOQ d A ~EBWQWMOB K(F w ~ A ~EBWQWMOQWMlC+LM��H�~+k : ~EL Q _ I y F?HWQ RJQ�~EQ�\mL ~Ew3Q<C+I(Q H<C+ImH � FJLmH<F32=((wlFk?C+L Q<FJL ~EL Q.I(L RJQ�~EQ)\mL ~Ew K(Fxwzy ~EI(Q<C/2 ~EQ<F|MOL(MOQWM ~Ew %

/.-,()*+}a

��b

##// GFED@ABC[ � <

a ..b �� /.-,()*+c

a

bb

bqq?>=<89:;76540123X

a

HH

b

cc

f C+Q<C+LmH�MlkJM!_ ImF�k?FJQ)~EI(Q<C/2 ~EQ<F�F?HWQ�wlF 2��32 F�� d I(L�B<FJLmC/2L2 ~E{PF�K(F%H<F?H�RJQ�~EQ<H A(B 0?H��P_ ImF�k?FJwOI(M C/((Q<FJL IA ~EB�w ~xk?C+LmH<QWBWImkJQWMlC+L K MOB<F?kJQ<F�� k?F�_ I(M(LmC+ImH%MOLmK M1_ ImF)_ ImF�wzy ~EwO{PC+BWMOQ@:�2 F.K(F;k?C+LmHWQWBWImkJQWMlC+L K MOB<F?kJQ<F.K(C+L(LmFK(F3Dz~EMOQ�wzy ~EI(Q<C/2 ~EQ<F*2 MOL(M'2 ~Ew %

� �� %|4 � / � /)4�6

D � # �"�� <�C+LmH<QWBWI(MOB<F wzy [ u�f B<F?k?C+L(L ~EMlH<H^~EL Q�wlF�w ~EL({ ~E{PF K(Rh\mL(MqA ~EB wzy Fh4 A(B<F?H<HWMlC+LoB<RJ{fI(wOM10JB<F ( +�� *�� +.- + +Q�FJL I(QWMOwOMlH�~EL Q;w ~ k?C+LmHWQWBWImkJQWMlC+L K(F*ab:mC/2 AmH<C+L %D � # �1D � <�C+LmH<QWBWI(MOB<FxI(L [ uHcgd A ~EBWQWMOB0K(F|wzy [ u�f A(B<C K I(MOQ d wzy Fh4(FJB<kJMlk?FxA(B<R?k?R?K(FJL Q %D � # �'i � <�C+LmH<QWBWI(MOB<FxI(L [ uHc K MOB<F?kJQ<F32 FJL Q d A ~EBWQWMOB0K(F|wzy Fh4qA(B<F?H<H<MlC+L B<RJ{fI(wOM10JB<F ( +�� *�� +.- + + %D � # �y� � ^ MOL(M'2 MlH<FJB;wzy [ u�c C/((Q<FJL I A C+I(B"( +�� *�� +.- + + FJL A ~+H<H^~EL Q;A ~EB�wzy [ u�f %

� ��

� �� T��8� �� #� � �� T��

^ ~EwO{fB<R5wlFJI(BvA CfH<H<M'((MOwOMOQ<R?Hvk?FJBWQ<F?HvwOM'2 MOQ<R?F?H�� w ~ A(I(MlH<H�~ELmk?FoK(F?HvFh4qA(B<F?H<H<MlC+LmH.B<RJ{fI(wOM10JB<F?HxFJL DGC+L QxK(F?H~EI54 MOwOM ~EMOB<F?H.QWB 0?H.MOL Q<RJB<F?H�H�~EL Q<HxFJL MOL D C+B@2 ~EQWM1_ ImF % c FxDz~EMOQ�� K(F�LmC/2,((B<FJI54 C+I(QWMOwlHvI(QWMOwOMlH<FJL Q3wlF?H.Fh4 A(B<F?H �HWMlC+LmH B<RJ{fI(wOM10JB<F?H ,%B<F?k;:mFJB<k :mF�FJQ B<F32 A(w ~+k?F32 FJL Q Km~ELmH wlF?H R?K MOQ<FJI(B<H K(F Q<Fh4qQ<F��k?C/2L2 ~ELmK(F?H t L(My4 �w ~EL({ ~E{PF?H�K(F H<kJBWMOA(Q<H � . FJBWw � . AqQ@:mC+LM� %'%'% � � wOM'((B�~EMOBWMlF K y Fh4 A(B<F?H<HWMlC+LmH|B<RJ{fI(wOM10JB<F?H K(F?Hxw ~EL({ ~E{PF?H�{PRJLmRJB�~F�wOMlHWQ<F?H�k?C/2L2 F � ~cN+~H� FJQ<k % <�F;k;: ~EA(MOQWB<FvN MlH<F d K(C+L(LmFJB%I(LmF0A(B<F32 M10JB<F0MOL QWB<C K ImkJQWMlC+L d k?FJQWQ<F0I(QWMOwOMlH�~EQWMlC+LK(F?H;Fh4 A(B<F?H<HWMlC+LmH�B<RJ{fI(wOM10JB<F?HvKm~ELmH�wlF?H;C+I(QWMOwlH.k?C+I(B�~EL Q<H %

:�� 2�@ � :��

j y C+I(QWMOw,u&vmw�u/x'F?HWQ wzy I(L K(F?H C+I(QWMOwlH wlF?H A(wOImH HWM'2 A(wlF?H d I(QWMOwOMlH�FJB wlF?H Fh4qA(B<F?H�HWMlC+LmH B<RJ{fI(wOM10JB<F?H % pswHcy ~E{fMOQ�K y I(LmF3k?C/2L2 ~ELmK(F3A C+A(I(w ~EBWMlH�R?FvH�C+ImH t L(My4p2 ~EMlHb2 ~EMOL Q<FJL ~EL Q0K MlHWA C+L(M'((wlF?H�H<C+ImH K(F.LmC/2,((B<FJI54H@A HWQ 032 F?HoK y Fh4qA(wlC+MOQ�~EQWMlC+L % � w ~ ( ~+H<F��)C+L wOI(M%DGC+I(BWL(MOQ FJL'FJL QWB<R?F I(LmF Fh4qA(B<F?H<H<MlC+L B<RJ{fI(wOM10JB<F FJQ5I(LmFwOMlHWQ<FxK(F \ k;:(MlFJB<H��mFJQ u&v�w5u&x B<FJQ<C+I(BWLmF|FJL B<R?HWI(wOQ�~EQ0Q<C+I(Q<F?H�wlF?H�wOMO{fLmF?H;K(F?Hb\ k;:(MlFJB<H0K y FJL QWB<R?F|C$; MOw ~5RJQ<RA CfH<HWM'((wlFxK y ~EA(A ~EBWMlFJB _ ImFJw1_ ImFxk :mCfH<F�~cNPF?k|wzy Fh4 A(B<F?H<HWMlC+L B<RJ{fI(wOM10JB<F %�. ~EBvFh4 F32 A(wlF��mH<M C+L DG~EMOQ!,

� umvmw�u/x��@��+��/|��{��{/u&w ��w ~5k?C/2L2 ~ELmK(FxNf~�QWB�~EMOQ<FJB�wlF \ k;:(MlFJB � �&|��{!�!��{/u/w��"�� wOMO{fLmF3A ~EB�wOMO{fLmF��(F?H<H^~ APFJB;K y ~EA(A ~EBWMlFJB;wzy Fh4 A(B<F?H �HWMlC+L B<RJ{fI(wOM10JB<F � +��# FJQ B<FJQ<C+I(BWLmFJB Q<C+I(Q<F?H wlF?H wOMO{fLmF?H C$; k?FJw ~�~EI(B�~�RJQ<R A CfH<HWM'((wlF % X L t L(My4 ��k?FJQWQ<Fk?C/2L2 ~ELmK(FxHcy MOL Q 0J{fB<F.A ~EB[Dz~EMOQ<F32 FJL Q;Km~ELmH�wzy F?HWA(BWMOQ�H<FJwlC+L wlF _ ImFJw wlF?H k?C/2L2 ~ELmK(F?H A(B<FJL(LmFJL Q;FJL FJL QWB<R?FK(F?H�\ k :(MlFJB<HvH<R _ ImFJL QWMlFJwlH3K(F�kc~EB�~+kJQ 0JB<F?HvFJQ0B<FJQ<C+I(BWLmFJL QxK(F?H)\ k :(MlFJB<H3H<R _ ImFJL QWMlFJwlH3K(F|kc~EB�~+kJQ 0JB<F?H % <�F?kJMA FJB@2 FJQ|K(C+Lmk K(FoA(MOA FJwOMOLmFJB�wlF?H|k?C/2L2 ~ELmK(F?H umvmw5u&x ~cNPF?k K y ~EI(QWB<F?H�k?C/2L2 ~ELmK(F?H t L(My4 � k?C/2L2 F A ~EBFh4(F32 A(wlFxw ~ok?C/2L2 ~ELmK(F%$Q� � A C+I(B&$'�&w!}e�(�*)�|��((MlFJL H��(B �h% j ~ k?C/2L2 ~ELmK(F�k?C/2 A CfH<R?F|HWI(MONf~EL Q<F�,

� umvmw�u/x��@��+��/|��{��{/u&w �� *+$��B<FJQ<C+I(BWLmF|QWB<C+MlH0LmC/2,((B<F?H � B<R?HWI(wOQ�~EL Q3K(F,$Q� � ,(wlF|LmC/2,((B<F�K(F*2 C+Q<H��mK(FxwOMO{fLmF?HvFJQ0K(F|kc~EB�~+kJQ 0JB<F?HvKm~ELmHwlF \ k :(MlFJB.B<R?HWI(wOQ�~EL QvK(F3w ~ k?C/2L2 ~ELmK(F umvmw�u/xj y C+I(QWMOw u&v�w5u/xB� k?C/2L2 F w ~ A(wOI(A ~EBWQ K(F?H C+I(QWMOwlHL_ I(M I(QWMOwOMlH<FJL Q wlF?H Fh4qA(B<F?H�HWMlC+LmHoB<RJ{fI(wOM10JB<F?H�� LmF H<F

wOM'2 MOQ<F|A ~+H3~EI54 Fh4qA(B<F?H�HWMlC+LmH0K(F�w ~oQ@:mR?C+BWMlF�Q<FJwOwlF?H _ ImFxLmC+ImH;wlF?H3~?NPC+LmH.N ImF?Hv~EI k;: ~EA(MOQWB<F�A(B<R?k?R?K(FJL Q %}�MlFJL _ ImF k?F?H Fh4 A(B<F?H<HWMlC+LmH B<RJ{fI(wOM10JB<F?H �Ekc~ELmC+L(M1_ ImF?H � H<C+MlFJL Q HWIHG H�~EL Q<F?H A C+I(B Fh4qA(BWM'2 FJB Q<C+ImH wlF?Hw ~EL({ ~E{PF?H B<RJ{fI(wOMlFJB<H��MOw0F?H<Q H<C+I(NPFJL Q A(B�~EQWM1_ ImF K y I(QWMOwOMlH<FJB K(F?H B�~+k?k?C+ImkJMlH % . ~EB Fh4(F32 A(wlF��HWM.C+L NPFJI(QFh4 A(BWM'2 FJB.wlF|DG~EMOQ _ I y C+L NPFJI(Q3~EA(A ~EBWMlFJBvI(LmF k?FJBWQ�~EMOLmF5Fh4 A(B<F?H<HWMlC+L B<RJ{fI(wOM10JB<F e C+I w ~ k : ~FElLmF N MlK(F�� C+L

-/. S10Od ]32 Y54!6�7zY[ZGZ/098i_%7":1;^X ] 09<57zY%Y[Z b>=?0 ZGY�Y[_?b/7zY U 6*8^Z b/7"8@6�AEYB6*8iX�7�:1CD0 bzY57 ]32 0 _?bzY57"6!7": b U b"098i_FEaY%ZGY Z�S U 7 U S b"<G7zY[ZH6 U 7 ]32 0 _�IbzY57"6!7": bzY[X�7�E!Y�S58@=?= U _JE!Y[Z[dPS Y V?XJ0(Y[Z b�Z/8^XJCJY _cb _J:[S[Y ZGZ U 0K7zY[Z ] 8L7zZzV?X 2 8i_ X!b"0 ] 0 ZGY?E!Y[Z�=?:sb U S U 7 U S b"<57zY Z�S18@=?=�Y%_J8^XEZ ] YCJY57/7"8^_EZ�6 ] X!Z ] 8L0 _�M

�� [ A(A(wOMlkc~EQWMlC+L K(F?H;Fh4 A(B<F?H<HWMlC+LmH;B<RJ{fI(wOM10JB<F?H

^ RJQ�~+kc~EB�~+kJQ 0JB<F [ A(A ~EBWMlF� L y M'2 A C+BWQ<F*_ ImFJw kc~EB�~+kJQ 0JB<F�H�~EI D w ~=\mL K(FxwOMO{fLmF %�� kJw ~+H�H<FxK(F|kc~EB�~+kJQ 0JB<F?H � Q<C+I(Q.kc~EB�~+kJQ 0JB<F�Km~ELmH�w ~ H�R _ ImFJLmk?FxFJL QWB<F�kJB<Cqk :mFJQ %�� kJw ~+H�H<FoK(F5kc~EB�~+kJQ 0JB<F?H�k?C/2 A(wlR32 FJL Q�~EMOB<F � Q<C+I(Q|kc~EB�~+kJQ 0JB<F H�~EI D�k?FJI54 Km~ELmH3w ~

H�R _ ImFJLmk?F %� < R?k;: ~EA(A F32 FJL Q0K(F 2 RJQ�~+kc~EB�~+kJQ 0JB<F �mHWM <3F?HWQ I(L�2 RJQ�~+kc~EB�~+kJQ 0JB<F��mMOw B<FJA(B<FJLmK H^~

H<MO{fL(My\ kc~EQWMlC+L LmC+B@2 ~EwlF|FJL Q�~EL Q�_ ImFxkc~EB�~+kJQ 0JB<F %� w ~5A CfHWMOQWMlC+L ~EI K(R3((I(Q.K(Fxw ~5wOMO{fLmF %� w ~5A CfHWMOQWMlC+L d w ~ \mL K(Fxw ~5wOMO{fLmF %�� w ~5A CfHWMOQWMlC+L ~EI K(R3((I(Q.K y I(L 2 C+Q %� � w ~5A CfHWMOQWMlC+L d w ~ \mL K y I(L 2 C+Q %* � ~EwOQ<FJBWL ~EQWMONPF � k?F _ I y ~EA(A ~EBWMlF w ~ H<C+ImH � Fh4 A(B<F?H<HWMlC+L K(F { ~EImk :mF'C+I w ~ H<C+ImH@�

Fh4 A(B<F?H<HWMlC+L K(F�K B<C+MOQ<F % � C+A(QWMlC+L �)Z C+I I(LmF3DGC+MlH�wzy ~EA(A ~EBWMlF32 FJL Q3K(F3w ~ H<C+ImH � Fh4 A(B<F?H<HWMlC+L %� � MOQ<RJB�~EQWMlC+LM� DGFJB@2 FJQWI(B<F ��Z � I(LmF�C+I A(wOImH<MlFJI(B<H;DGC+MlH;wzy ~EA(A ~EBWMlF32 FJL Q3K(F�w ~ H<C+ImH@�

Fh4 A(B<F?H<HWMlC+L %� I(LmF�C+I A(wOImHWMlFJI(B<H�DGC+MlH�wzy ~EA(A ~EBWMlF32 FJL Q3K(F3w ~ H<C+ImH@� Fh4qA(B<F?H<H<MlC+L %� # T @ � #�2 �� FJL QWB<F # T @ D C+MlH0FJQ:#�2 DGC+MlH�wzy ~EA(A ~EBWMlF32 FJL Q3K(F3w ~ H<C+ImH@� Fh4qA(B<F?H<H<MlC+L %()- {fB<C+I(A F32 FJL Q.wOM'2 MOQ�~EL Q.w ~5A C+BWQ<R?F|FJQ0I(QWMOwOMlH<R3A C+I(B0wlF?H�B<RiD RJB<FJLmk?F?Hv~EBWBWM10JB<F?H %�i I(LmFxLmC+I(NPFJwOwlFxD C+MlH;k?F+_ I(M�~oRJQ<R�~EA(A ~EBWMlR|A ~EB;wlF i

M1032 F {fB<C+I(A F %�� 75%'$ � . BWMOLmkJMOA ~EI54 2 RJQ�~+kc~EB�~+kJQ 0JB<F?HvK(F?H0Fh4qA(B<F?H<H<MlC+LmH�B<RJ{fI(wOM10JB<F?H0K(F|FJ{fB<FJA

A FJI(Q;Fh4qA(BWM'2 FJBvk?FJw ~oK(Fxw ~ 2 ~EL(M10JB<F�HWI(MONf~EL Q<F&,(e|ε)

<�F {PFJL(B<F K y Fh4qA(B<F?H<H<MlC+L�_ I(M�k :mFJB<k :mF HWM'2 A(wlF32 FJL Q d Fh4 A(BWM'2 FJB�wlFoDz~EMOQ,_ ImFowzy ~EA(A ~EBWMlF32 FJL Q K(F e F?HWQC+A(QWMlC+L(LmFJw � K(FJN MlFJL Q�NqMOQ<F3~+H<H<F��0wlC+I(B<K d R?kJBWMOB<FvFJQ d wOMOB<F % u&vmw�u/xoA(B<C+A CfH<F0A(wOI(Q��+Q�wzy C+A RJB�~EQ<FJI(B3y y A C+I(BHWMO{fL(My\ FJB;wzy C+A(QWMlC+L(L ~EwOMOQ<R�� k?F+_ I(M LmC+ImH;A FJB@2 FJQWQWB�~EMOQ0K y R?kJBWMOB<F|MlkJM ,

e

c F�2��32 F��(H<M C+L NPFJI(Q.R?kJBWMOB<F+_ I y d I(L k?FJBWQ�~EMOL FJLmK B<C+MOQ0C+L NPFJI(Q0~EA(A ~EBWMlFJB0Q<C+I(Q<F?H�wlF?H 2 MOL ImH�kJI(wlF?H��MOw Dz~EImK B�~EMOQ0R?kJBWMOB<F�Km~ELmH�w ~5NPFJB<H<MlC+L kc~ELmC+L(M1_ ImF=,(;�* + *@��* } *�u&* z * v */� * { *�� *�� *��*"� *J| *��&*Jx *�� * w * ~�* � * ) *�� * $ * � *�� *�� -

k?F _ I(M)F?HWQ�((MlFJL H��(BvwlC+L({ FJQ0DG~+HWQWMlK MlFJI54 % u&vmw�u/x A FJB@2 FJQvK y R?kJBWMOB<FoK(F?HvkJw ~+H<H<F?HvK(F kc~EB�~+kJQ 0JB<F?HxH<C+ImH.w ~DGC+B@2 FxK y I(LmF|H<R _ ImFJLmk?F|K(Fxkc~EB�~+kJQ 0JB<F?H0FJL QWB<F�kJB<Cqk :mFJQ<H % � L A FJI(Q;K(C+Lmk|R?kJBWMOB<FxwlF?H;wlFJQWQWB<F?H)2 MOL ImH�kJI(wlF?HH<C+ImH�w ~ DGC+B@2 F�,

� � +��F}5u&z�v��{��B|'�/x��w�~J��)��$��

<�FJQWQ<F DGC+B@2 F N+~#~EA(A ~EBWMlFJB Fh4(~+kJQ<F32 FJL Q I(L kc~EB�~+kJQ 0JB<F A ~EB@2 M0w ~ wOMlHWQ<F % X wOwlF F?HWQ K(R � d I(L A FJI'A(wOImHk?C/2 A ~+kJQ<F 2 ~EMlH FJLmk?C+B<F Dz~+HWQWMlK MlFJImH<F %�. B<C�\mQ�~EL Q K I Dz~EMOQL_ ImF wzy ~EwOA�: ~�( FJQoF?H<Q5B<FJA(B<R?H�FJL Q<R FJL [ n�<�p�pFJQ�FJL w ~EQWMOL5� $ A ~EB K(F?H k?C K(F?H�L I�2 RJBWM1_ ImF?H H�R _ ImFJL QWMlFJwlH��Humvmw5u&x A FJB@2 FJQ K y R?kJBWMOB<F K(F?H|MOL Q<FJBWN+~EwOwlF?HoK(Fkc~EB�~+kJQ 0JB<F?H5FJL�HWA R?kJMy\ ~EL Q�wlF A(B<F32 MlFJB5FJQ|wlF K(FJBWL(MlFJB kc~EB�~+kJQ 0JB<F Km~ELmH�wzy C+B<K B<F L I�2 RJBWM1_ ImF K(F?H�k?CqK(F?H��H<RJA ~EB<R?H�A ~EB0wlFxQWMOB<FJQ|y � y % � L A FJI(Q;K(C+LmkxQ<C+I(Q.HWM'2 A(wlF32 FJL QvR?kJBWMOB<F�,

� �!�"� �

k?F _ I(M F?HWQvLmFJQWQ<F32 FJL QxA(wOImHxk?C+L DGC+BWQ�~�((wlF % � L A FJI(Q|~?NPC+MOB3A(wOImHWMlFJI(B<H3MOL Q<FJBWN+~EwOwlF?HxKm~ELmH3I(LmF5kJw ~+H<H<FoK(F

75%'$ j y C+I(QWMOw�u&vmw�u/x �&W

kc~EB�~+kJQ 0JB<F?H %�[ MOLmHWM �� !�"��

Nf~ ~EA(A ~EBWMlFJB.Fh4m~+kJQ<F32 FJL Q0I(L kc~EB�~+kJQ 0JB<F�A ~EB@2 M wlF?H 2 MOL ImH<kJI(wlF?H.FJQ�wlF?H)2 ~F� ImH<kJI(wlF?H %pskJM � wlF�kc~EB�~+kJQ 0JB<F QWMOB<FJQvF?HWQ0A(BWMlHv~cNPF?k�I(L H<FJLmH0A ~EBWQWMlkJI(wOMlFJB�� k?F _ I(M H�F32,((wlF5F32 AB�?k;:mFJBvK(F wzy MOLmkJwOI(B<F

Km~ELmH I(LmF kJw ~+H<H<F K(F kc~EB�~+kJQ 0JB<F ~?NPF?k H<C+L H<FJLmH C+BWMO{fMOL ~Ew �%kfy F?H<Q � d � K MOB<F ~EA(A ~EBWMlFJB wlF kc~EB�~+kJQ 0JB<F QWMOB<FJQ %c FoDz~EMOQ�� MOw%Fh4qMlH<Q<FoI(LR2 CPAPFJL K(F k?C+L Q<C+I(BWLmFJBok?FJw ~., HWM%C+L#NPFJI(Q ~cNPC+MOB�I(LmF kJw ~+H�H<F K(F kc~EB�~+kJQ 0JB<Fp_ I(M~EA(A ~EBWMlF ~EImH<HWM)wlF5kc~EB�~+kJQ 0JB<FoQWMOB<FJQ�� MOw�Dz~EI(QvA(w ~+k?FJB3wlFokc~EB�~+kJQ 0JB<FoQWMOB<FJQ|~EI K(R3((I(QxK(F5w ~ kJw ~+H<H<F�� k?C/2L2 FA ~EB0Fh4(F32 A(wlF|Km~ELmH:,

� ��

_ I(M N+~ ~EA(A ~EBWMlFJB.wlF3QWMOB<FJQ0C+I wlFxH<C+I(wOMO{fLmR %p wmFh4 MlHWQ<F0~EImH<H<M(I(LmF.~EI(QWB<F DGC+B@2 F�MOL Q<RJB<F?H�H�~EL Q<FvK(F?H%kJw ~+H<H�F?H�K(F;kc~EB�~+kJQ 0JB<F?H ,+w ~xkJw ~+H<H<F;K(F0kc~EB�~+kJQ 0JB<F?H

k?C/2 A(wlR32 FJL Q�~EMOB<F % � I ~ELmK I(LmF kJw ~+H<H�F K(F kc~EB�~+kJQ 0JB<F?H k?C/2L2 FJLmk?F A ~EB wlF kc~EB�~+kJQ 0JB<F kc~EB<FJQ y � yW� ~EwlC+B<HFJwOwlF ~EA(A ~EBWMlFoLmC+L A ~+H3wlF?Hxkc~EB�~+kJQ 0JB<F?H|Km~ELmH3w ~ wOMlHWQ<F 2 ~EMlH3Q<C+I(Q|kc~EB�~+kJQ 0JB<F K I �WFJI K(F kc~EB�~+kJQ 0JB<F H�~EI Dk?FJI54 _ I(M�~EA(A ~EB�~EMlH�H<FJL Q0Km~ELmH0w ~5wOMlHWQ<F % j ~ kJw ~+H<H<F

� � �!� ��

~EA(A ~EBWMlF5K(C+Lmk|Q<C+I(Q3kc~EB�~+kJQ 0JB<F H�~EI D�wlF?H.wlFJQWQWB<F?H�2 ~F�[ImH<kJI(wlF?HvFJQ�2 MOL ImH<kJI(wlF?H % u&vmw�u/x K(Rh\mL(MOQ0A(wOImH<MlFJI(B<HkJw ~+H<H<F?H K(F kc~EB�~+kJQ 0JB<F?H�H<FJwlC+LoI(LmF H@AqL Q�~F4(F �� @Q'$#� �� +k?C+LmHWI(wOQ<F�� w ~.A ~E{PF�K(F 2 ~EL ImFJwmK(F)u&v�w5u&xA C+I(B�wlF?H�k?C+L(L ~FElQWB<F % psw!A�~3~EImH<H<M I(L ~EI(QWB<Fb2 RJQ�~+kc~EB�~+kJQ 0JB<F QWB 0?H)I(QWMOwlF ,EwlF>2 RJQ�~+kc~EB�~+kJQ 0JB<F|y ��y � wlF�A C+MOL Q �_ I(M HWMO{fL(My\ F�~EA(A ~EBWMlFJB0Q<C+I(Q.kc~EB�~+kJQ 0JB<F|H�~EI D w ~ \mL K(FxwOMO{fLmF %j ~=\m{fI(B<F 75%'$ B<R?HWI�2 F3wlF?H�A(BWMOLmkJMOA ~EI54 2 RJQ�~+kc~EB�~+kJQ 0JB<F?H0K(F,umvmw�u/x % � C+ImH��JQ<F?H MOL N MOQ<R?H d k?C+LmHWI(wOQ<FJB

w ~vA ~E{PF�K(Fb2 ~EL ImFJw K(F umvmw�u/x�A C+I(B�C/((Q<FJL(MOB�A(wOImH�K y MOL DGC+B@2 ~EQWMlC+LmH d k?F�HWI/�WFJQ � DG~EMOB<Fxy ��/| u&v�w5u/x y+H<C+ImHt L(My4 �h% t Lok?C+Lmk?FJA(Q�MOL Q<RJB<F?H<H�~EL Q�A ~EB@2 Mqk?F?HU2 RJQ�~+kc~EB�~+kJQ 0JB<F?H�F?HWQ)k?FJwOI(MqK(F�A CfH<MOQWMlC+LmH ~EA(A ~EBWMlR?F?H)A ~EB K(F?H2 RJQ�~+kc~EB�~+kJQ 0JB<F?H % j F 2 RJQ�~+kc~EB�~EQ 0JB<F y � yW� wlC+B _ I y MOw�F?HWQ3I(QWMOwOMlH<R FJL�K(F3:mC+B<HxK y I(LmF kJw ~+H�H<FoK(F kc~EB�~+kJQ 0JB<F?H��HWMO{fL(My\ F|FJL Dz~EMOQ�_ I y MOw DG~EI(Q0~EA(A ~EBWMlFJB.wlFxK(R3((I(Q.K y I(LmFxwOMO{fLmF %�. ~EB0Fh4(F32 A(wlF��

� ��w �F� �L y ~EA(A ~EBWMlFJB�~ w ~ H<R _ ImFJLmk?F K(F kc~EB�~+kJQ 0JB<F?H yK��w �� y�_ ImF H<M k?FJwOwlFh� kJM;~EA(A ~EB�~FElQ ~EI'K(R3((I(Q K y I(LmF wOMO{fLmF %j F?H 2 RJQ�~+kc~EB�~+kJQ 0JB<F?H y � yW� y �� y(FJQ|y � � yF�[C+ImFJL Q;wlF�2��32 F3B��+wlF3A C+I(B�B<F?H<A F?kJQWMONPF32 FJL Q0w ~,\mL K(F3wOMO{fLmF��(wlFK(R3((I(Q0K y I(L 2 C+Q.FJQ�w ~ \mL K y I(L 2 C+Q %

� � $�� #%� � � � � �

n M�w ~ A(wOI(A ~EBWQ5K(F?H ~F�WC+I(Q<H ~EI54�Fh4qA(B<F?H�HWMlC+LmH|B<RJ{fI(wOM10JB<F?H5kJw ~+H<HWM1_ ImF?HxLmF H�C+L Q,_ ImF K I �6 ��H< �(*& >" @ �8 2 $T � ��* � � kfy F?HWQ � d � K MOB<F�I(LmF|H@AqL Q�~F4(F3A(wOImH0HWM'2 A(wlF|A C+I(B;R?kJBWMOB<F*_ ImFJw1_ ImF|k :mCfH<F,_ I(M ~EI(B�~EMOQ.A(I Hcy R?kJBWMOB<FKm~ELmH�w ~3H@AqL Q�~F4(F�kJw ~+H<HWM1_ ImF��u&v�w5u&x|DGC+I(BWL(MOQ�I(LmF0~EI(QWB<F;k?C+LmHWQWBWImkJQWMlC+Lp_ I(MmF?HWQ�QWB 0?H�A(I(MlH�H�~EL Q<F;FJQ�FJLoDz~EMOQFJL�K(F3:mC+B<H5K(F?H�Fh4 A(B<F?H<HWMlC+LmH�B<RJ{fI(wOM10JB<F?H , wlF {fB<C+I(A F32 FJL Q A ~EB A ~EB<FJL Q@:�0?H<F?HoFJQ|w ~ B<RiD RJB<FJLmk?F ~EBWBWM10JB<F %j F?H A ~EB<FJL Q@:�0?H<F?HoA FJI(NPFJL Q �JQWB<F wOM'( RJB�~EwlF32 FJL QoI(QWMOwOMlH<R?F?H5A C+I(B K(RJwOM'2 MOQ<FJB5w ~ A C+BWQ<R?F K(F?H5C+A RJB�~EQ<FJI(B<H��k?C/2L2 FxA ~EB0Fh4(F32 A(wlF|Km~ELmH:,(;� +�� -

_ I(M H<MO{fL(My\ F|~EA(A ~EBWMlFJB;C+A(QWMlC+L(LmFJwOwlF32 FJL Q0w ~5H<R _ ImFJLmk?F,� +�� % n ~ELmH wlF?H A ~EB<FJL Q@:�0?H�F?H�� wzy C+A RJB�~EQ<FJI(B y yqLmFHcy ~EA(A(wOM1_ ImFJB�~EMOQ _ I y ~EI kc~EB�~+kJQ 0JB<FN� � MOw�~5A(wOImH DGC+BWQ<FxA(BWMlC+BWMOQ<R*_ ImF3wzy C+A RJB�~EQ<FJI(BvK(Fxk?C+Lmkc~EQ<RJL ~EQWMlC+L �h%

<�FJA FJLmKm~EL Q��EC+I(QWB<F k?F%B��+wlF�K(F�K(RJwOM'2 MOQ�~EQWMlC+L K(F�w ~0A C+BWQ<R?F��!wlF?H)A ~EB<FJL Q@:�0?H<F?H FJLNu&v�w5u/xxH<C+L Q I(QWMOwOMlH<R?F?HA C+I(B0wlF|B<FJ{fB<C+I(A F32 FJL QxFJQ.wlF?H0B<RiDGRJB<FJLmk?F?Hx~EBWBWM10JB<F?H.Fh4 A(BWM'2 R?F?HvA ~EB0w ~ H A L Q�~F4 F y � i y C$; i B<RiDJ0JB<F i

032 F{fB<C+I(A FxB<F?k?C+L(L I K(FJA(I(MlH;wlFxK(R3((I(Q0K(Fxwzy Fh4 A(B<F?H<HWMlC+L B<RJ{fI(wOM10JB<F %�. ~EBvFh4 F32 A(wlF��

7&Z [ A(A(wOMlkc~EQWMlC+L K(F?H;Fh4 A(B<F?H<HWMlC+LmH;B<RJ{fI(wOM10JB<F?H

( � � � � � -�� Nf~ ~EA(A ~EBWMlFJB K y ~�( C+B<K I(L�kc~EB�~+kJQ 0JB<F A ~EB@2 M%wlF?H3wlFJQWQWB<FL2 MOL(MlH<kJI(wlF?H�� A(I(MlHxI(LmFoB<RJA RJQWMOQWMlC+L�K(F Z � $ � C+IA(wOImHWMlFJI(B<Hvkc~EB�~+kJQ 0JB<F?H+_ ImFJwlk?C+L�_ ImF?HvH�~EI D�w ~ \mL K(F|wOMO{fLmF�� A(I(MlH d LmC+I(NPFc~EI wlF=2��32 F�kc~EB�~+kJQ 0JB<F _ I(M)~RJQ<RvB<F?k?C+L(L I A ~EB�wlFvA(B<F32 MlFJB�{fB<C+I(A FvA ~EB<FJL Q@:mR?H<R %�. C+I(B0H�~cNPC+MOB d _ ImFJw {fB<C+I(A F.I(L MOLmK Mlk?F i H<F.B<RiD 0JB<F��MOw(Dz~EI(Q�k?C/2 A(Q<FJB K(F�{ ~EImk :mF d K B<C+MOQ<F0wlF?H�A ~EB<FJL Q@:�0?H<F?H C+I(N B�~EL Q<F?H�FJQ�QWB<C+I(NPFJB%wlF;{fB<C+I(A F;MOL QWB<C K I(MOQ�A ~EBw ~ i

032 F A ~EB<FJL Q@:�0?H<F�C+I(NqB�~EL Q<F % p w F?HWQ�((MlFJL H��(B;A CfH<HWM'((wlFxK y M'2,((BWM1_ ImFJB0wlF?H;A ~EB<FJL Q@:�0?H<F?H %j ~|B<RiDGRJB<FJLmk?F.~EBWBWM10JB<F.L y F?HWQ�A ~+H�Fh4 A(BWM'2 ~�((wlF.Km~ELmH�wlF?H�Fh4qA(B<F?H<H<MlC+LmH%B<RJ{fI(wOM10JB<F?H�Q@:mR?C+BWM1_ ImF?H�� Km~ELmH�w ~

2 F?HWI(B<F|C$; wlF|Q<Fh4qQ<F3B<F?k?C+L(L I Km~ELmH;I(L {fB<C+I(A F32 FJL QvK(C+MOQ �JQWB<F+2 R32 C+BWMlH<FJB % <�C+L QWB�~EMOB<F32 FJL Q d k?F*_ I(MH<F3A ~+H<H�F|Km~ELmH�w ~oB<F?k?C+L(L ~EMlH<H^~ELmk?F|A ~EB0Fh4 A(B<F?H<HWMlC+LmH�B<RJ{fI(wOM10JB<F?H.Q@:mR?C+BWM1_ ImF?H��(w ~L_ I ~EL QWMOQ<R K(F+2 R32 C+MOB<FLmR?k?F?H<H�~EMOB<F A C+I(B0B<FJA(B<R?H<FJL Q<FJBvwlF�Q<Fh4qQ<F B<F?k?C+L(L I L y F?HWQ.A ~+H�( C+BWL ~�((wlF % p w L y F?HWQvK(C+Lmk A ~+H.A CfH<H<M'((wlF�K(FB<Rc~EwOMlH<FJBxw ~ B<RiDGRJB<FJLmk?F ~EBWBWM10JB<F Km~ELmHxI(L�~EI(Q<C/2 ~EQ<F K y RJQ�~EQ<H+\mL(M % <vy F?HWQxA ~EB<k?FL_ ImFow ~ B<F?k?C+L(L ~EMlH<H^~ELmk?FF?HWQxDz~EMOQ<FoA ~EB|I(L�C+B<K MOL ~EQ<FJI(BoK(F A(wlFJMOL�K B<C+MOQ�� FJQ�K(C+Lmkp_ I y MOw�F?HWQ|A CfH<HWM'((wlF K y ~cNPC+MOBo~+k?k 0?H d Q<C+I(Q<F w ~A(I(MlH<H�~ELmk?F K(F�k?F�K(FJBWL(MlFJB��&_ I y MOw F?HWQ�A CfH<HWM'((wlF�FJLNu&vmw�u/x|K(F�A(B<C+A CfH�FJB k?F?H)B<RiDGRJB<FJLmk?F?H�~EBWBWM10JB<F?H�FJQ)K y C / BWMOB~EMOLmHWM I(LmFxA(I(MlH�H�~ELmk?F|HWQWBWMlkJQ<F32 FJL Q0A(wOImH�{fB�~ELmK(F=_ ImFxk?FJwOwlF|K(F?H0Fh4qA(B<F?H<H<MlC+LmH�B<RJ{fI(wOM10JB<F?H.kJw ~+H�HWM1_ ImF?H %

� A(B<C+A CfH K(F?H B<RiDGRJB<FJLmk?F?H ~EBWBWM10JB<F?H Km~ELmH wlF?H Fh4qA(B<F?H<H<MlC+LmH �!B<RJ{fI(wOM10JB<F?H �� MOw3A FJI(Q �JQWB<F I(QWMOwlF#K(F2 R?K MOQ<FJB w ~ A�:(B�~+H<F.H<I(MON+~EL Q<F.QWB<C+I(NPR?FxKm~ELmH�w ~ K(C kJI�2 FJL Q�~EQWMlC+L K(F?H Fh4qA(B<F?H�HWMlC+LmH�B<RJ{fI(wOM10JB<F?H�HWQ�~ELmKm~EB<K. � nqp � � H<C+ImH j MOL I54 � ,

�� 2 < �P* ��* �P*>@Q<7*� �2 �(* 2 � �P*(2 �� ) %('�8 <>4 � 3H' �TA@ #�2��9'�� 3�� ' %>)W*9#� � ' �N*�� <9T *>@58&T # �3B)W*>#&*>@Q8 2�8UTU'�@ � > 4 *>" 2��(* 2$) 9'= '$#&* � 42�8 �F2� � *9) " �6* �J@B*�� 6'�*� �y� � ( � ( + � - � �� - � } �#�2�8 <94 �y��+�+�+B} �� '$T � � �TA@&8A4 *># � �

:�� 2|@ � 4�6 / � ! !�-;= #54�6 4)@ � 2|@ � :<6 � = � %

. wOImHWMlFJI(B<H�k?C/2L2 ~ELmK(F?H�FJQ�C+I(QWMOwlH�K MlHWA C+L(M'((wlF?H�H<C+ImH t L(My4oFJQ A ~EB[DGC+MlH�H<C+ImH�K y ~EI(QWB<F?H%H AqHWQ 032 F?H�K y Fh4B�A(wlC+MOQ�~EQWMlC+L I(QWMOwOMlH<FJL Q�wlF?H Fh4 A(B<F?H<HWMlC+LmH�B<RJ{fI(wOM10JB<F?H % c ~ELmH�k?FJQWQ<F3H<F?kJQWMlC+LM�qLmC+ImH FJL A ~EB<k?C+I(B<C+LmH _ ImFJw1_ ImF?HI(LmH;K(FxA(wOImH0K(C+L Q0wzy I(QWMOwOMOQ<R|A FJI(Q;Hcy ~cNPRJB<FJB _ ImC+QWMlK MlFJL(LmF %

�� %� � #%# ��

j ~ k?C/2L2 ~ELmK(F t L(My4�z�{`|B} H<FJBWQ d w ~5B<F?k;:mFJB<k :mF5K(F \ k :(MlFJB<H.Km~ELmH;I(LmF�:(MlRJB�~EB<k :(MlF5K(F3B<RJA FJBWQ<C+MOB<F?H %nqC+L'H@AqLmC+A(QWM1_ ImF MOLmK M1_ ImF�_ ImF k?FJQWQ<F k?C/2L2 ~ELmK(F A(B<FJLmK K(FJI54 ~EBW{fI�2 FJL Q<H , wlF A(B<F32 MlFJB F?HWQoI(L'C+IA(wOImHWMlFJI(B<H.k :mF32 MOLmH.MOLmK M1_ I ~EL Q.wlF?H�B�~+kJMOLmF?HvK(F?H�B<RJA FJBWQ<C+MOB<F?H d A ~EB<k?C+I(BWMOB�� FJQ;wlF|H�F?k?C+LmK ~EBW{fI�2 FJL Q3F?HWQI(LmF;k?C/2L2 ~ELmK(F d ~EA(A(wOM1_ ImFJB � A ~EB%K(RiDz~EI(Q��PHcy MOwmL y A ~3A ~+H%K(F�k?C/2L2 ~ELmK(F d ~EA(A(wOM1_ ImFJB��z�{F|!} M'2 A(BWM'2 FHWM'2 A(wlF32 FJL Q0wlF?H�LmC/2 H.K(F?Hb\ k :(MlFJB<H0QWB<C+I(NPR?H %j ~ k?C/2L2 ~ELmK(FNz�{F|!} F?HWQvQWB 0?H3{PRJLmRJB�~EwlF � FJwOwlFoA FJB@2 FJQ3K(F DGC+I(MOwOwlFJBxK(F?H3B<RJA FJBWQ<C+MOB<F?HxA C+I(B3QWB<C+I(NPFJB

K(F?H=\ k :(MlFJB<H FJL D C+LmkJQWMlC+L'K(F wlFJI(BoLmC/21��wlFJI(B5Q�AqA F�� wlFJI(Bo{fB<C+I(A F K y ~EA(A ~EBWQ<FJL ~ELmk?F��A ~EB5wlFJI(BoQ�~EMOwOwlF��A ~EB�wlFJI(B Km~EQ<F K(F K(FJBWL(M10JB<Fp2 C K My\ kc~EQWMlC+LM�)FJQ<k % <�C+LmH<I(wOQ<F�� wlFL2 ~EL ImFJw�FJL�wOMO{fLmF � y ��&| z�{`|B} y � A C+I(B~?NPC+MOB3A(wOImHxK(F5K(RJQ�~EMOwlHxHWI(B3k?FJQWQ<F k?C/2L2 ~ELmK(F % j y C+A(QWMlC+L �`w5umvBu(� A FJB@2 FJQxK(F�B<F?k;:mFJB<k :mFJB�K(F?H \ k;:(MlFJB<HA ~EB|~EA(A ~EBWMlF32 FJL Q�K(F5wlFJI(B3LmC/2 ~?NPF?koI(LmFoFh4 A(B<F?H<HWMlC+L B<RJ{fI(wOM10JB<F % t L A C+MOL QxK(RJwOMlkc~EQ d HWI(BWNPFJMOwOwlFJB|F?HWQ_ ImFxwlF3LmC/2�K(F�\ k;:(MlFJB0I(QWMOwOMlH<R|F?H<Q;wlF3LmC/2�k?C/2 A(wlFJQ��mMOLmkJwOI ~EL Q.wlFxk;:mF32 MOL K(F?H;B<RJA FJBWQ<C+MOB<F?H.k?C+L Q<FJL ~EL QwlF \ k :(MlFJB %j F?H�Fh4qA(B<F?H�HWMlC+LmH B<RJ{fI(wOM10JB<F?H � H<C+ImH w ~.Nf~EBWM ~EL Q<F�K(F j MOL I545MOLmH<Q�~EwOwlR?F�HWI(B�2 ~+k :(MOLmF � HWI(MONPFJL Q�wlF�LmC+B@2 F. � nqp � � DG~EMOB<F y ��/|�� w5u&v5u(� y �h%

75% �L[ I(QWB<F?H;k?C/2L2 ~ELmK(F?HvFJQ;C+I(QWMOwlH t L(My4 75$

�� %� � #%# ��

j y C+I(QWMOw)~mu&} F?HWQ|I(L�R?K MOQ<FJI(B5K(F Q<Fh4 Q<F �F:mC+B<H|wOMO{fLmF��R_ I(M�A FJB@2 FJQ�K y R?kJBWMOB<F K(F?H|H<kJBWMOA(Q<H K y R?K MOQWMlC+LK(F=\ k :(MlFJB<HxA(I(MlHxK(F5wlF?H3Fh4(R?kJI(Q<FJB|H<C+ImHvwzy MOL Q<FJBWA(B<RJQ<FJI(B K(Fok?C/2L2 ~ELmK(F C+I#FJLmk?C+B<F k?C/2L2 F5A(B<C k?F?H�HWImHt L(My4#FJL ~EBWBWM10JB<F A(w ~EL � K(C+Lmk H�~ELmH|MOL Q<FJB[DG~+k?F ~?NPF?k wzy I(QWMOwOMlH^~EQ<FJI(B �h% <vy F?HWQ K(C+Lmk I(LmF k?C/2L2 ~ELmK(F QWB 0?HI(QWMOwlF.wlC+B<H _ I y MOw Hcy ~E{fMOQ K(F0B<Rc~EwOMlH�FJB K(F?H�R?K MOQWMlC+LmH A C+MOL QWImF?H 2 ~EMlH�B<RJA RJQWMOQWMONPF?H HWI(B�I(L M'2 A C+BWQ�~EL Q {fB<C+I(A FK(F�\ k;:(MlFJB<H � A FJI(Q �S�JQWB<F|H<RJwlF?kJQWMlC+L(LmR?H.A ~EB�I(LmF|k?C/2L2 ~ELmK(F,z�{`|!} �h%j y R?K MOQ<FJI(B*~mu&} F?H<Q�B<FJw ~EQWMONPF32 FJL Q3k?C/2 A(wOM1_ ImR d I(QWMOwOMlH<FJB % c FxA(wOImH��(C+L wOI(M A(B<RiD 0JB<F|K(FxA(wOImH0FJL A(wOImH

K(F?H�H<kJBWMOA(Q<H%R?kJBWMOQ<H�Km~ELmH�K(F?H�w ~EL({ ~E{PF?H�K(F0H<kJBWMOA(Q<H�k?C/2L2 F . FJBWw C+I . AqQ@:mC+L % c ~ELmH�wlF?H�{fB�~ELmK(F?H�wOMO{fLmF?H��~&um} Hay ~EA(A(wOM1_ ImF d I(LL\ k;:(MlFJB�FJL wlF;K(R?k?C+I(A ~EL Q�FJL Q�~�2 A C+LmH>_ I(M k?C+BWB<F?HWA C+LmK(FJL Q�FJL {fB<CfH d K(F?H%wOMO{fLmF?H %<>: ~/_ ImF;Q�~�2 A C+L F?HWQ%k;: ~EBW{PR0FJL�2 R32 C+MOB<F�� A(I(MlH%wlF?H%k?C/2L2 ~ELmK(F?H�K y R?K MOQWMlC+LmH�K(C+L(LmR?F?H�Km~ELmH�I(L H<kJBWMOA(Q~&um}oH<C+L Q;~EA(A(wOM1_ ImR?F?H % j C+B<H _ ImF.wlF?H k?C/2L2 ~ELmK(F?H�C+L Q RJQ<Rv~EA(A(wOM1_ ImR?F?H��qwlF;Q�~�2 A C+L B<R?HWI(wOQ�~EL Q�F?HWQ�k?C+A(MlRKm~ELmH�wlF�\ k;:(MlFJB0B<R?HWI(wOQ�~EL Q��(A(I(MlH0C+L A ~+H�H<F|~EI Q�~�2 A C+L HWI(MONf~EL Q %j y MOL Q<RJBP�JQ0K(F,~&um} Km~ELmH wlF.k?C+L Q<Fh4qQ<FxK(F?H Fh4 A(B<F?H<HWMlC+LmH B<RJ{fI(wOM10JB<F?H NqMlFJL Q�K(F3k?F _ ImFvwzy C+L A FJI(Q R?kJBWMOB<F

K(F?H k?C/2L2 ~ELmK(F?H)K(F�B<F?k;:mFJB<k :mF�FJQ B<F32 A(w ~+k?F32 FJL Q�C$;|wlF�Q<Fh4 Q<F�B<F?k;:mFJB<k :mR F?HWQ ~EA(A ~EBWMlR d I(LmF%Fh4 A(B<F?H<HWMlC+LB<RJ{fI(wOM10JB<F % <�FJQWQ<F DGC+LmkJQWMlC+L(L ~EwOMOQ<R;LmC+ImH%C / B<F I(LmF A(B<F32 M10JB<F;Cqk?kc~+HWMlC+L K(F A ~EBWwlFJB%K y I(LmF;LmC+I(NPFJwOwlF�I(QWMOwOMOQ<RK(F?H {fB<C+I(A F32 FJL Q<H%Km~ELmH wlF?H�Fh4 A(B<F?H<HWMlC+LmH B<RJ{fI(wOM10JB<F?H ,Ew ~0A CfH<HWM'((MOwOMOQ<R�K y I(QWMOwOMlH�FJB�wlF?H A C+BWQWMlC+LmH�K(F�k;: ~FElLmF?HB<F?k?C+L(L ImF?H;A ~EB;k : ~+kJI(L K(F?H {fB<C+I(A F?H;~EA(B 0?H wzy ~EA(A ~EBWMlF32 FJL Q�� FJQ�K(C+Lmk3MlkJM A C+I(B k?C+LmH<QWBWI(MOB<F3wlF.Q<Fh4 Q<FxK(FB<F32 A(w ~+k?F32 FJL Q %H[ NPF?k I(LmF H@AqL Q�~F4(F HWM'2 MOw ~EMOB<F d k?FJwOwlF K(F?H�B<RiD RJB<FJLmk?F?H5~EBWBWM10JB<F?H � 2 ~EMlH*_ I(M�L y FJL�H<C+L QA ~+H3A(I(MlH _ I y FJwOwlF?H3LmFoH<C+L Q3A(wOImHvI(QWMOwOMlH<R?F?HxKm~ELmH3wzy Fh4 A(B<F?H<HWMlC+L B<RJ{fI(wOM10JB<F � C+L A FJI(Q3B<RiDGRJB<FJLmk?FJBxwlF Q<Fh4 Q<FB<F?k?C+L(L I Km~ELmH�I(L {fB<C+I(A F %�. ~EB0Fh4 F32 A(wlF�� w ~ok?C/2L2 ~ELmK(F�HWI(MONf~EL Q<F&,

~&u&} �/u � ~�� ( �� - � � � ( �� -� � � � �� &v �p��/|��{��{/u&w ��A(B<FJLmK B�~�wlFb\ k :(MlFJB � �&|��{!�!��{/u/w��"��oFJQ�k?C+L NPFJBWQWMOB�~�wlF?H�LmC/2,((B<F?H�K(R?kJM'2 ~EI54 FJL LmC+Q�~EQWMlC+L ~�2 RJBWMlkc~EMOLmF� ~?NPF?k�wlF3A C+MOL Q0K(R?kJM'2 ~Ew � FJL LmC+Q�~EQWMlC+L D B�~EL��c~EMlH�F � ~?NPF?k|w ~5NqMOBW{fI(wlF|K(R?kJM'2 ~EwlF �h%

�� &� ��

� ��m~ F?HWQ�I(L R?K MOQ<FJI(B K(F Q<Fh4qQ<F Fh4qQ<FJLmHWM'((wlF R?kJBWMOQ FJL j MlHWA�_ I(M�K(C+MOQ5H�~ {fB�~ELmK(F A C+A(I(w ~EBWMOQ<R LmC+LH<FJI(wlF32 FJL Qx~EI Dz~EMOQ _ I y MOw D I(Qvwzy I(L K(F?HvA(B<F32 MlFJB<HxR?K MOQ<FJI(B<H3A(wlFJMOL R?kJB�~EL 2 I(wOQWM D FJL��JQWB<R�� 2 ~EMlHx~EImH<HWM�~EIDz~EMOQH_ I y MOw(F?HWQ)C+I(NPFJBWQ��P~EI H<FJLmH C$;5MOw(F?HWQ�B<FJw ~EQWMONPF32 FJL Q�Dz~+kJMOwlF�K(F K(Rh\mL(MOB�K(F�LmC+I(NPFc~EI54=2 CqK(F?H K y R?K MOQWMlC+L~?NPF?k Q<C+I(Q<F|w ~ A(I(MlH<H�~ELmk?F K(F j MlHWA % k?FJw ~ Nf~ K I H<M'2 A(wlF,2 CqK(F3D B�~EL��c~EMlH _ I(M A FJB@2 FJQ.K(F k?C/2 A CfH<FJB.wlF?Hkc~EB�~+kJQ 0JB<F?Ho~+k?k?FJL QWImR?H LmC+L5� K MOB<F?kJQ<F32 FJL Q K MlHWA C+L(M'((wlF?H5~EI�kJw ~cN MlFJB�� ImH;_ I y ~EI 2 CqK(F ��}Bu K y R?K MOQWMlC+L K(F� ~cN+~ _ I(M�A(B<C+A CfH<FoA(wOImHWMlFJI(B<H K(F?H3D C+LmkJQWMlC+L(L ~EwOMOQ<R?H _ ImFowzy C+L�B<FJQWB<C+I(NPF Km~ELmHxwlF?H FJL NqMOB<C+L(LmF32 FJL Q<HoK(FA(B<C+{fB�~�2L2 ~EQWMlC+L�RJNPC+wOImR?H � 2 FJL ImH�~+Km~EA(Q�~EQWM D H3A FJB@2 FJQWQ�~EL Q|K(F5B<FJQWB<C+I(NPFJBxB�~EA(MlK(F32 FJL Q|I(L \ k :(MlFJB|C+II(LmF3K(Rh\mL(MOQWMlC+L Km~ELmH I(L�\ k :(MlFJB��(MOLmH�FJBWQWMlC+L K(F.A ~EQWB<C+LmH0H@A L Q�~F4qM1_ ImF?H�� k?C/2 A(MOw ~EQWMlC+LM�mFh4(R?kJI(QWMlC+LM�(FJQ<k % �h%

� ��m~ C / B<F K(F�LmC/2=((B<FJImH<F?H DGC+LmkJQWMlC+LmH I(QWMOwOMlH^~EL Q#wlF?H Fh4qA(B<F?H�HWMlC+LmH B<RJ{fI(wOM10JB<F?H��xK(C+L Q wzy I(L K(F?HFh4(F32 A(wlF?H.F32=((wlR32 ~EQWM1_ ImF?HxF?HWQ.w ~ k?C/2L2 ~ELmK(F5K(F B<F?k :mFJB<k :mFoFJQvB<F32 A(w ~+k?F32 FJL Q3MOL Q<FJB�~+kJQWMONPF ~cNPF?k Fh4B�A(B<F?H<HWMlC+L B<RJ{fI(wOM10JB<F�~EA(A FJwlR?F|A ~EB!,

� �D� ��)5u/w��`w5u/x!��/u!�`w5umvBu(�C$; � Km~ELmH�wlF��<~EBW{PC+L�u��5��~3F?H<Q�w ~3Q<C+Imk :mF�2 RJQ�~x{PRJLmRJB�~EwlF32 FJL Q�B<Rc~EwOMlH<R?F0A ~EB�w ~3Q<C+Imk;:mF0R?k : ~EA(A F32 FJL Q� C+I F?H<kc~EA F � HWI(B�wlF|kJw ~cN MlFJB %j ~ H A L Q�~F4 F K(F?H0Fh4 A(B<F?H<HWMlC+L B<RJ{fI(wOM10JB<F?H3K y u��5��~ F?HWQ�2 ~Ew':mFJI(B<FJImH<F32 FJL Q|K M0/ RJB<FJL Q<F K(F?HvH@AqL Q�~F4(F?H

NqImF?HO�[ImH _ I y MlkJM % r0FJ{ ~EB<K(F��vw ~ K(C kJI�2 FJL Q�~EQWMlC+L FJL wOMO{fLmFvK y uF��m~xA C+I(B ~cNPC+MOB�A(wOImH K(F0K(RJQ�~EMOwlH % <�FJA FJL5�� Y54!0 Z b U 0 b Y[_xY"!PYsb U C U _?b>=$#1=�Y ] Y[Z�:[S57 U _EZ>; 7 U 6�AJ0 V?XEY[Z[dfYsb>0 ] 6fY57"=�Y bGb U 0 bHE!:&%(' U CJY[SBE!Y Z>:[S57 U _EZ�6EX�7zY5=�Y[_?bbzY54cbzXEY ] Z S18L=?=�Y ] Y�C?b*)Wg^g&E 2 : E!0 bzYG7�X!_.bzY54cbzY�Y[_ 6 ] Y10 _,:[SG7 U _3Y b�=$#1=�Y+'�ZGX, E!09C!0 ZGY57 S[Ysb�: S57 U _3Y _ 6 ] X!Z/0 Y X�7zZ ` Y[_-# b/7zY[ZAJ8 7"0/.18i_?b U^] Y1=�Y _cb Ysb�CiY57Gb"0 S U^] Y1=�Y[_?b 0

7 � [ A(A(wOMlkc~EQWMlC+L K(F?H;Fh4 A(B<F?H<HWMlC+LmH;B<RJ{fI(wOM10JB<F?H

Km~EL Q�� k?C/2L2 F|A C+I(B;w ~oB<F?k;:mFJB<k :mFoFJQ;B<F32 A(w ~+k?F32 FJL Q3K(F ~mu&}5�mw ~oA ~EBWQWMlF|B<F?k;:mFJB<k :mF A FJB@2 FJQvK y I(QWMOwOMlH<FJBK(F?H5Fh4qA(B<F?H<H<MlC+LmH�B<RJ{fI(wOM10JB<F?HoFJQ5MOw�F?HWQ A CfH<H<M'((wlF K y I(QWMOwOMlH<FJB5wlF?H�B<RiDGRJB<FJLmk?F?H��+~EBWBWM10JB<F?H ��Km~ELmH w ~ A ~EBWQWMlFB<F32 A(w ~+k?F32 FJL QvA C+I(B�B<Rc~EwOMlH<FJB;I(LmF|R?K MOQWMlC+L k?C+L Q<Fh4qQWImFJwOwlF5K y I(L K(CqkJI�2 FJL Q %

:� � 4�684 %�� 4�6 6 �� =56 � � �02 : � � 4�6 # 4 � 4 � :

j F�w ~EL({ ~E{PF . FJBWw�~ B<RJNPC+wOI(QWMlC+L(LmR5wlF,2 C+LmK(F5K(F?H0w ~EL({ ~E{PF?H3K(F5H<kJBWMOA(Q<H d w ~N\mL K(F?H3~EL(LmR?F?H5y �&Z FJQK(F32 FJI(B<F;~EI/�WC+I(B<K y : I(M � ~cNPF?k . A Q@:mC+LN_ ImF�LmC+ImH�RJNPC!_ ImFJB<C+LmH d w ~vH<F?kJQWMlC+L HWI(MON+~EL Q<F��+wzy I(L K(F?H w ~EL({ ~E{PF?HK(F�H<kJBWMOA(Q<H wlF?H A(wOImH A C+A(I(w ~EMOB<F?H % t Lxw ~EL({ ~E{PF�K(F�H<kJBWMOA(Q<H F?HWQ I(L|w ~EL({ ~E{PF�K(C+L Q wlF B��+wlF�A(BWMOLmkJMOA ~Ewqk?C+LmHWMlHWQ<Fd 2 ~EL(MOA(I(wlFJBoK(F?H5H<R _ ImFJLmk?F?H K(F kc~EB�~+kJQ 0JB<F?H��)k : ~FElLmF?HoFJQ wlF A(wOImH5H<C+I(NPFJL QoK(F?H+\ k;:(MlFJB<H % psw%LmF Hcy ~E{fMOQA ~+H5MlkJM�K(F Dz~EMOB<F I(L k?C+I(B<H K(F . FJBWw;FJL H<C+M % j F?H5wlF?kJQ<FJI(B<HoMOL Q<RJB<F?H<H<R?H H�C+L Q5A(BWMlR?H K(F H<F B<RiDGRJB<FJB d w ~K(CqkJI�2 FJL Q�~EQWMlC+L�K(F . FJBWw � NPC+MOB.A ~EB3Fh4(F32 A(wlF . FJB�~ �� A C+I(Bx~?NPC+MOBvI(LmF�MlK(R?F {PRJLmRJB�~EwlF5K(F k?F w ~EL({ ~E{PF %j y MOL Q<RJBP�JQ K(F0A ~EBWwlFJB�K(F . FJBWw MlkJM B<R?HWMlK(F.F?H�H<FJL QWMlFJwOwlF32 FJL Q Km~ELmH�wlF0DG~EMOQ _ ImF0w ~|H@AqL Q�~F4(F0K(F?H�Fh4qA(B<F?H�HWMlC+LmHB<RJ{fI(wOM10JB<F?HxK(F . FJBWw�F?H<QvFJL NPC+MlF5K(F5K(FJNPFJL(MOBxI(L HWQ�~ELmKm~EB<K �6* �92 <�8 ' _ I(M A FJB<k?C+wlF5H<I(B.wzy FJLmH<F32=((wlF K(F?HC+I(QWMOwlH % j ~5K(CqkJI�2 FJL Q�~EQWMlC+L K(F . FJBWw A(B<R?H�FJL Q<F|~EImH<HWM I(LmF3K(F?H<kJBWMOA(QWMlC+L K(F3H�~�H A L Q�~F4 F3K(F?H Fh4qA(B<F?H�HWMlC+LmHB<RJ{fI(wOM10JB<F?H . FJB@( ��%t LmF0{fB�~ELmK(F0A ~EBWQWMlFvK(F?H 2 RJQ�~+kc~EB�~+kJQ 0JB<F?H _ ImF;LmC+ImH ~?NPC+LmH�NqImHO�[ImH _ I y d 2 ~EMOL Q<FJL ~EL Q0~EA(A ~EB�~EMlH<H<FJL Q

Fh4m~+kJQ<F32 FJL Q�K(F�w ~)2��32 F�Dz~$�?C+L Km~ELmH�wlF?H�Fh4 A(B<F?H<HWMlC+LmH B<RJ{fI(wOM10JB<F?H . FJBWw % j y ~EL QWMy� C/((wOM1_ ImF H<FJBWQ d A(B<C+Q<RJ{PFJBwlF?H 2 RJQ�~+kc~EB�~+kJQ 0JB<F?H�A C+I(B�wlFJI(B B<F?K(C+L(LmFJB�wlFJI(B HWMO{fL(My\ kc~EQWMlC+L FJL Q�~EL Q _ ImFvHWM'2 A(wlF3kc~EB�~+kJQ 0JB<F % j F3kc~EB<FJQ� y � y � K(R?HWMO{fLmF.w ~xA CfHWMOQWMlC+L FJL K(R3((I(Q�K(F0wOMO{fLmF��q~EwlC+B<H _ ImF0wlF0K(C+wOw ~EB � y � y � K(R?HWMO{fLmF0w ~|A CfH<MOQWMlC+L FJLN\mL K(FwOMO{fLmF % wlF�A C+MOL Q � y �^y � ~EA(A ~EBWMlF Q<C+I(Q.kc~EB�~+kJQ 0JB<F5H�~EI D�w ~ \mL K(F|wOMO{fLmF % j y ~EwOQ<FJBWL ~EQWMONPF5F?H<Q.K(RJLmC+Q<R A ~EB0w ~NPFJBWQWMlkc~EwlF � y�*<y � �PwlF�B<FJ{fB<C+I(A F32 FJL Q�A ~EB�wlF?H%A ~EB<FJL Q@:�0?H<F?H�FJQ�wlF?H%kJw ~+H�H<F?H%K(F;kc~EB�~+kJQ 0JB<F?H�A ~EB�wlF?H�kJB<C k;:mFJQ<H %c FN2��32 F�� wlF A C+MOL Q K y MOL Q<FJBWB<C+{ ~EQWMlC+L HWMO{fL(My\ F wzy C+A(QWMlC+LM��wzy ~+HWQ<RJBWMlH _ ImF wlF D FJB@2 FJQWI(B<F K(F��3wlF?FJLmF FJQ�wlFA(wOImH�w ~5DGFJB@2 FJQWI(B<FxA CfHWMOQWMONPF %

c F?H k?C/2L2 ~ELmK(F?H�K(R3((I(Q�~EL Q#A ~EB ~EL QWMy� C/((wOM1_ ImF'K(R?H<MO{fLmF k?FJBWQ�~EMOLmF?H#kJw ~+H�H<F?H K(F kc~EB�~+kJQ 0JB<F?H�� _ I(MA FJI(NPFJL Q0~EImH<HWM �JQWB<F3A(B<R?K(Rh\mL(MlF?H0A ~EB;K(F?H LmC/2 H _ ImFvwzy C+L A FJI(Q�I(QWMOwOMlH<FJB0~?NPF?k3w ~5H@AqL Q�~F4(F ��

〈 @B'$# 〉 � � �k?C/2L2 F|Km~ELmH �� )!x�x�u/w �� A C+I(B�w ~ kJw ~+H<H<FxK(F?H0kc~EB�~EQ 0JB<F?H.~EwOA�: ~�( RJQWM1_ ImF?H�2 ~F� ImH<kJI(wlF?H %

�"��# # �� $&�� &� ��

. ~EB@2 M(wlF?H k?C/2L2 ~ELmK(F?H�K(F . FJBWwqI(QWMOwOMlH^~EL Q�wlF?H Fh4qA(B<F?H�HWMlC+LmH B<RJ{fI(wOM10JB<F?H��EMOw5A ~;wlF�Q<F?HWQ K y ~EA(A ~EBWMlF32 FJL Q_ I(M H<F3A(B<R?H<FJL Q<F K(F3w ~ 2 ~EL(M10JB<F|HWI(MONf~EL Q<F&,

{Fz ( � w5u/x'�/|�~&u�� - �

x!w�{`|��/�!��{Fz!zmw5u5~ ~mu()!��uF��u/|�� |�� u�B~mu �

x!w�{`|��3x5�5~ ~&u()!��u��u/|�� }5uB~ �!��{Fz!zmw5u5~ � |��

j F�Q<F?HWQ)K y RJ{ ~EwOMOQ<R ��;~EA(A ~EBWMlF wlF�k?C+L Q<FJL I K(F�w ~0N+~EBWM ~�((wlF � w5u/x'�/|�~&u �!A(B<R?HWI�2 R32 FJL Q�I(LmF k : ~FElLmF�wOImF~EI5Q<FJB@2 MOL ~Ew �+~cNPF?k�wzy Fh4qA(B<F?H<H<MlC+L B<RJ{fI(wOM10JB<F�FJL QWB<F�C/((wOM1_ ImF �!wlFT� K(FJNf~EL Q w ~0A(B<F32 M10JB<F�C/((wOM1_ ImF�MOLmK M1_ I ~EL Q_ I y MOw Hcy ~E{fMOQ0K(F3Dz~EMOB<F3I(LmFxQ<FJL Q�~EQWMONPF K y ~EA(A ~EBWMlF32 FJL Q %j F?H;B<FJ{fB<C+I(A F32 FJL Q<H.A FJI(NPFJL Q �JQWB<FxI(QWMOwOMlH�R?H0FJL . FJBWw � ~?NPF?k k?C/2L2 F ~cN+~EL Q�~E{PF,_ ImF3wlF?H;A C+BWQWMlC+LmH0K(F

k : ~FElLmF?HvB<F?k?C+L(L ImF?H3A ~EBvk;: ~+kJI(L K(F?H.{fB<C+I(A F?HvH�FJB<C+L Qx~+k?k?F?H<HWM'((wlF?HvKm~ELmHvK(F?H.Nf~EBWM ~�((wlF?H.LmC/2L2 R?F?H �� %'%'%�[ MOLmHWM �(C+L A FJI(Q.R?kJBWMOB<F�,

x�w�{F|�� |��!w5u��)!| ��/|��5�/|�� u*� )�|5u ��/|�|��5{&u � ��

75%87 j F?H0Fh4qA(B<F?H<H<MlC+LmH�B<RJ{fI(wOM10JB<F?H.K(F . FJBWw 7&7

� w5u&x �&|�~&u�� {`w5u �!�ow/x'�/|�~mu �() �5u&w&�Q{F|5��!� ��Bx ( � w�u/x'�/|�~mu - � � u&|��5u �� z�{`| }Bu �5{�vm|�u z�{`|��u }5u � w5u&x �/|�~&u{Fz ( � w5u/x'�/|�~&u�� ( ��

�� -.( � � � � -� - �

� � �/|��5�&|�� /|!|5��{/u�� {�z ( � ��/|�|��5{&u u � D� �- � �e�*�/|��u/w�~!{(�&| }Bu zmw��/|��~ u/| u()!w �B~

� |'�()�� &|��5�&|�� &|��/|��

x�w�{`|��Bz��B� � z u()!w �B~ � |� � � |'�()�� &|��5�&|��

� u��5~&u � �e�*�/|��u/w�~!{(�&| }��@u*)�w'�B~ u/| zmw��/|��m~� |'�()�� &|��5�&|�� &|��/|��

x�w�{`|��Bz��B� � z zmw��/|��~ � |� � � | �()� � �/|��/|��

�� u�B~mu �

x!w�{`|�� 5~*�� &|�|��5{/u {F|��(�&|�|�)5u � |��

f C+Q<C+LmHvQ<C+I(QvA ~EBWQWMlkJI(wOM10JB<F32 FJL Q|Km~ELmH3k?F�A FJQWMOQvA(B<C+{fB�~�2L2 F wzy I(QWMOwOMlH^~EQWMlC+L K(F?H.Nf~EBWM ~�((wlF?H �� FJQ � ��[ImHWQ<Fv~EA(B 0?H�wzy ~EA(A ~EBWMlF32 FJL Q;A C+I(B�B<R?kJI(A RJB<FJB�w ~|A C+BWQWMlC+L K(F.k;: ~FElLmF|~EA(A ~EBWMlR?F.A ~EB wlF?H K(FJI54 B<FJ{fB<C+I(A Fh�2 FJL Q<H3Km~ELmH0wzy Fh4qA(B<F?H<H<MlC+L B<RJ{fI(wOM10JB<F %Q. C+I(B3Fh4(R?kJI(Q<FJBvk?F�A(B<C+{fB�~�2L2 F�� MOw)HWIHG Q.K(F�wlF|QWB�~ELmH<kJBWMOB<F5Km~ELmHI(LmF�\ k;:(MlFJB��mA ~EB;Fh4(F32 A(wlFL�(�&|��5u&w�~B{(�/|�� x!w�� A(I(MlH.K y I(QWMOwOMlH<FJB;w ~ok?C/2L2 ~ELmK(F,x5u/w!� � H<C+ImH j MOL I54 � ,

� x�u/w!� �*�/|�5u/w�~!{*�/| ��x�w!�� |��!w5u � )!| � �/|��5�&|�� u(� )�|�u ��/|!|5�5{&u � �B��*�� u()�w'�B~

p w F?HWQ;~EImH<HWM A CfH�HWM'((wlF3K(F0B<F32 A(w ~+k?FJB;wlF)� Km~ELmH w ~ �Ek?C/2 A ~EB�~EMlH<C+L�� ~cNPF?k � �3A ~EB I(L ~� k?F�_ I(M NPFJI(Q~EwlC+B<H�K MOB<F LmC+L�A(wOImH�K(F DG~EMOB<F I(L HWM'2 A(wlF ~EA(A ~EBWMlF32 FJL Q��2 ~EMlH K(FoDG~EMOB<F I(LmF HWI�(mHWQWMOQWI(QWMlC+L % c ~ELmH�k?Fkc~+H��fC+L A FJI(Q%~EImH<HWM(I(QWMOwOMlH�FJB�wlF?H�{fB<C+I(A F?H % n I(A(A CfH�C+LmH _ ImF NPC+ImH�~ AqMlF��0H�~EMlHWM(I(L Q<Fh4 Q<F;FJLL: Q@2 w C$; NPC+ImH~?NPF��,2 ~EwlFJLmk?C+L QWB<FJImH<F32 FJL QvI(QWMOwOMlH�R|Fh4qA(wOMlkJMOQ<F32 FJL Q0w ~ 2 MlH�FxFJL MOQ�~EwOM1_ ImF � � { � � A(wOI(Q��+Q�_ ImF3wzy F32 A�: ~+H<F� � u�� h% j y ~EA(A(wOMlkc~EQWMlC+L K(F�w ~ HWI�(mHWQWMOQWI(QWMlC+L#HWI(MONf~EL Q<F5B<F32 A(w ~+k?F5A C+I(BvI(L Q<Fh4 Q<F�wlF?H ( ~EwOMlH<F?H3MOQ�~EwOM1_ ImF?HA ~EB0K(F?H ( ~EwOMlH�F?H;K y F32 A�: ~+H<F � FJL H<I(A(A CfH�~EL Q)_ ImF3wlF|Q<Fh4qQ<FxFJL MOQ�~EwOM1_ ImFxLmF|k?C+L QWMlFJL Q0A ~+H;wOI(My� 2��32 F�K(F( ~EwOMlH<F � ,

� �5u*��u � � ~�� { � ( � � �� - �� { � � � u�� "�� u�� &v �

j F?Ho~EL QWMy� C/((wOM1_ ImF?H � � � H<FJBWNPFJL Q5MlkJM d A(B<C+Q<RJ{PFJB wlF?H5C/((wOM1_ ImF?H � � � K(F?H,( ~EwOMlH�F?H�A C+I(B=_ ImF . FJBWw�LmF wlF?Hk?C+L DGC+LmK(FxA ~+H0~?NPF?k�wlF?H;C/((wOM1_ ImF?H;K(RJwOM'2 MOQ�~EL Qvwzy Fh4qA(B<F?H�HWMlC+L B<RJ{fI(wOM10JB<F|FJQ;wlF3Q<Fh4 Q<F|K(F3B<F32 A(w ~+k?F32 FJL Q %

�)�� &� � �� $�� '� ��

. FJBWw ~F�WC+I(Q<F.FJLmk?C+B<F3K(F.LmC+I(NPFJwOwlF?H�Fh4 Q<FJLmHWMlC+LmH�~EI54 Fh4 A(B<F?H<HWMlC+LmH�B<RJ{fI(wOM10JB<F?H _ I(M LmF;DGC+L Q�A ~+H�A ~EBWQWMlFK(F?H�Fh4 A(B<F?H<HWMlC+LmH B<RJ{fI(wOM10JB<F?H0~EI H<FJLmH�Q@:mR?C+BWM1_ ImF|K I Q<FJB@2 F % j y I(LmFxK(Fxk?F?H�Fh4 Q<FJLmHWMlC+LmH QWB 0?H A(I(MlH<H�~EL Q<F?HF?HWQ wzy ~EL QWMlkJMOA ~EQWMlC+LM�.kfy F?HWQ � d � K MOB<F�w ~ Dz~+kJI(wOQ<R�K(F NPRJBWMy\ FJB HWMxI(L�Q<Fh4 Q<F�Hcy ~EA(A ~EBWMlF d I(LmF�Fh4 A(B<F?H<HWMlC+LB<RJ{fI(wOM10JB<F ~cN+~EL Q0K(FxA(B<Cqk?R?K(FJB d I(L ~EA(A ~EBWMlF32 FJL Q.A ~EBWQWMlFJw % j ~ H@AqL Q�~F4(FxF?HWQ:,( � e -

_ I(M0F?HWQ MOL Q<FJBWA(B<RJQ<R?F k?C/2L2 F wlF Dz~EMOQ K(F NPRJBWMy\ FJB HWM d I(LmF k?FJBWQ�~EMOLmF A CfHWMOQWMlC+L Km~ELmH wlF Q<Fh4qQ<F MOwvF?HWQA CfH<HWM'((wlF K y ~EA(A ~EBWMlFJB e �U2 ~EMlH5H�~ELmH k?C+LmH�C/2L2 FJBoF>/ F?kJQWMONPF32 FJL Q K(F Q<Fh4qQ<F % n I(A(A CfH<C+LmH�A ~EBoFh4(F32 A(wlF_ ImF wzy C+L NPFJI(MOwOwlF B<F32 A(w ~+k?FJBowlF A C+MOL Q K(R?kJM'2 ~Ew Km~ELmH�wlF?H LmC/2,((B<F?H K y I(L Q<Fh4 Q<FN2 ~EMlHoFJL RJNqMOQ�~EL Q K(F

7�] [ A(A(wOMlkc~EQWMlC+L K(F?H;Fh4 A(B<F?H<HWMlC+LmH;B<RJ{fI(wOM10JB<F?H

k?C+L DGC+LmK B<F;wlF�A C+MOL QT\mL ~Ew K y I(LmF�A�:(B�~+H<F % n I(A(A CfH<C+LmH>_ ImF LmC+ImH%A C+I(NPC+LmH�K MlHWQWMOL({fImFJB%wlF?H�K(FJI54 kc~+H�A ~EBwlFoDz~EMOQ,_ I y I(L�A C+MOL Q K(R?kJM'2 ~Ew�F?HWQ|Q<C+I/�WC+I(B<H�HWI(MONqM%K y ~EIR2 C+MOLmH�I(L k :(M0/ B<F K(F Z d W5% j ~ k?C/2L2 ~ELmK(FHWI(MONf~EL Q<FxNf~ Dz~EMOB<Fxw ~oHWI�(mHWQWMOQWI(QWMlC+L ,

� �5u*��u � � ~��( �� - ( �

� � �� -

� �'( �� -�

� � � �� &v �

[ A(B 0?Hx~?NPC+MOB�~EA(A ~EBWMlR5I(LmFoH<R _ ImFJLmk?F K y ~EI 2 C+MOLmH3I(L k :(M0/ B<F�� C+L NPRJBWMy\ FoHWM C+L A FJI(Qx~EA(A ~EBWMlFJBxI(LA C+MOL Q HWI(MON M K y ~EI�2 C+MOLmH�I(L k :(M0/ B<F % n M C+I(M � wzy ~EA(A ~EBWMlF32 FJL Q0H�F�Dz~EMOQ�A(I(MlH�C+L I(QWMOwOMlH�F0wlF?H K(FJI54 A C+BWQWMlC+LmHK(FxQ<Fh4 Q<F|~EA(A ~EBWMlR?F?H;A C+I(B;B<F?k?C/2 A CfH<FJB;wlF3LmC/2,((B<F5~?NPF?k�w ~5N MOBW{fI(wlF|K(R?kJM'2 ~EwlF %

:�� 4 ! � # �:<4 � ��m4)@ #54 � �v@�� = 4)@�,v-��-

� ~?Nf~oFJQ . A Q@:mC+L A ~EBWQ�~E{PF3I(LmFvNqMlHWMlC+L K(F?H�Fh4qA(B<F?H<H<MlC+LmH�B<RJ{fI(wOM10JB<F?H)2 C K(RJwOMlH<R?F?H A ~EB�K(F?H�C/(5�WFJQ<H % j ~A(B<C 4 M'2 MOQ<R�FJL QWB<FxwlF?H;K(FJI54 LmC+ImH�MOLmkJMOQ<F d wlF?H�QWB�~EMOQ<FJB0FJL A ~EB�~EwOw10JwlF %j F w ~EL({ ~E{PF . AqQ@:mC+L'F?HWQ��)k?C/2L2 F . FJBWw � wzy I(L K(F?H w ~EL({ ~E{PF?H K(F H<kJBWMOA(Q wlF?H5A(wOImH A C+A(I(w ~EMOB<F?H d k?F

�WC+I(B % j y ~?Nf~EL Q�~E{PF ~+k?k?C+B<K(R d . A Q@:mC+L HWI(B . FJBWw;NqMlFJL Q K I DG~EMOQL_ ImF . A Q@:mC+L F?HWQ k?C+LmHWMlK(RJB<R k?C/2L2 FI(L w ~EL({ ~E{PF d C/(5�[FJQ<H�� ~cNPF?koQ<C+I(Q<F?HxwlF?H3NPFJBWQWImF?H|~+H<H<CqkJMlR?F?H d k?F Q A A FoK(F5w ~EL({ ~E{PF?H|K I A C+MOL Q|K(F NqImFHWQWBWImkJQWI(B�~EQWMlC+L FJQ�B<RJI(QWMOwOMlH^~EQWMlC+L % <�FJw ~ DG~EMOQ;K(F . A Q@:mC+LM�(FJL A(wOImH;K y I(L w ~EL({ ~E{PF�K(FxH<kJBWMOA(Q�� I(L w ~EL({ ~E{PFK(F|A(B<C+Q<C+Q A A ~E{PFo~EA(A(B<R?kJMlR�� FJL A ~EBWQWMlkJI(wOMlFJB3A ~EB0wlF?H.k :mFJB<k :mFJI(B<HxKm~ELmH.wlF?H0K(C/2 ~EMOLmF?H3K I H AqHWQ 032 F�� K(F?Hw ~EL({ ~E{PF?H�K(F�A(B<C+{fB�~�2L2 ~EQWMlC+L C+I Km~ELmH�wlF�QWB�~EMOQ<F32 FJL Q�K(F?H�K(C kJI�2 FJL Q<H %�. C+I(B%A(wOImH�K y MOL D C+B@2 ~EQWMlC+L HWI(B. AqQ@:mC+LM� MOw�F?HWQ�A CfH<HWM'((wlF K(F k?C+LmHWI(wOQ<FJB�wlF HWMOQ<F MOL Q<FJBWLmFJQ _ I(M%wOI(M�F?HWQ�k?C+LmH�~+kJB<R � NPC+MOB . AqQ ��h% <�F HWMOQ<Fk?C+L QWMlFJL Q;RJLmC+B@2 R32 FJL Q;K y MOL DGC+B@2 ~EQWMlC+LmH;HWI(B�wlF0w ~EL({ ~E{PF?H�� FJQ FJL A ~EBWQWMlkJI(wOMlFJB;H^~|K(CqkJI�2 FJL Q�~EQWMlC+L FJQ H<F?HK MlHWQWBWM'((I(QWMlC+LmH %j F3w ~EL({ ~E{PF*� ~cN+~5L y ~5A(wOImH�{fI�0JB<F�( F?H<C+MOL K y �JQWB<F3A(B<R?H<FJL Q<R�� d k?F?kJM A(B 0?H)_ ImFvwlF3A ~/_ ImFJQ�~E{PFxK(F?H;Fh4B�

A(B<F?H<HWMlC+LmH%B<RJ{fI(wOM10JB<F?H �!��)��{��w5u&v5u(�oF?HWQ%wOMONqB<R;FJL HWQ�~ELmKm~EB<K K(FJA(I(MlH�w ~3NPFJB<HWMlC+L $&% ]�%8Z K I w ~EL({ ~E{PF %c y ~EI(QWB<F?H|A ~/_ ImFJQ�~E{PF?H|K(F QWB�~EMOQ<F32 FJL Q K(F?H|Fh4 A(B<F?H<HWMlC+LmHxB<RJ{fI(wOM10JB<F?H Fh4qMlH<Q<FJL Q|FJQ�H<C+L Q|K MlHWA C+L(M'((wlF?H ~EIQ<RJwlR?k : ~EBW{PF32 FJL QxHWI(B�wzy MOL Q<FJBWLmFJQ %

X L � ~?Nf~H�)wlF A ~/_ ImFJQ�~E{PF �!��5��)��{��w5umvBu(� A(B<C+A CfH<F K(FJI54 kJw ~+H<H<F?H5A C+I(B {PRJB<FJBow ~ A(wOI(A ~EBWQ K(F?HDGC+LmkJQWMlC+LmH�HWI(B wlF?H�Fh4qA(B<F?H<H<MlC+LmH B<RJ{fI(wOM10JB<F?H�,��B�(��5u&w�||FJQ � �*��!��u/w % j ~vQWB�~EMOQ<F32 FJL Q�A ~EB I(LmF�Fh4 A(B<F?H<HWMlC+LB<RJ{fI(wOM10JB<F�H<I(A(A CfH<F3{PRJLmRJB�~EwlF32 FJL Q.w ~oH�R _ ImFJLmk?F|K y ~+kJQWMlC+LmH.HWI(MONf~EL Q<F�,

$&% j y MOLmHWA F?kJQWMlC+L FJQ w ~ k?C/2 A(MOw ~EQWMlC+L K(F#wzy Fh4 A(B<F?H<HWMlC+L�B<RJ{fI(wOM10JB<F�FJL�I(LmF#D C+B@2 F MOL Q<FJBWLmFR_ I(MxNf~Dz~EMOB<F5K(F?Hv~EA(A ~EBWMlF32 FJL Q<H|FJL K MlH<QWMOL({fI ~EL Q�2 ~F� ImH�kJI(wlF?HvFJQ 2 MOL ImH<kJI(wlF?H�� k?F _ I(M�K(C+L(LmF5I(L C/(5�WFJQ�!A ~EQWB<C+L�� MOLmHWQ�~ELmk?F|K(Fxw ~okJw ~+H�H<F��B�*��5u&w�| %

�5% j y ~+H<H<CqkJM ~EQWMlC+L K y I(L Q<Fh4qQ<F d ~EA(A ~EBWMlFJB��(I(LmFxk;: ~FElLmFxK(Fxkc~EB�~+kJQ 0JB<F?H�A ~EB;Fh4 F32 A(wlF��(k?F+_ I(M K(C+L(LmFI(L C/(5�[FJQ0~EA(A ~EBWMlF32 FJL Q.MOLmHWQ�~ELmk?F�K(Fxw ~okJw ~+H<H<F � �(��5u&w %

75% j y Fh4 R?kJI(QWMlC+L K(Fvwzy ~EA(A ~EBWMlF32 FJL Q.HWI(B wzy MOLmHWQ�~ELmk?FxK(F � �*��5u/w A C+I(B NPRJBWMy\ FJB;HWM ~EA(A ~EBWMlF32 FJL Q0MOwQA~ FJQ;FJL k?C+LmHWQWBWI(MOB<FxwlF3B<R?HWI(wOQ�~EQ %

]�% n M wzy ~EA(A ~EBWMlF32 FJL Q�Hcy F?HWQ�DG~EMOQ�� B<FJLmK B<F.K MlHWA C+L(M'((wlF?H�wlF?H�MOL DGC+B@2 ~EQWMlC+LmH�HWI(B�k?FJQ�~EA(A ~EBWMlF32 FJL Q��qK(C+L QwlF|Q<Fh4qQ<F|~EA(A ~EBWMlR�A ~EB�wlF?H�B<FJ{fB<C+I(A F32 FJL Q<H %

<�F?H�C+A RJB�~EQWMlC+LmH�H<C+L Q%B<Rc~EwOMlH<R?F?H�A ~EB�wlF A(B<C+Q<Cqk?C+wlF0H<I(MON+~EL Q%Km~ELmH�wlF�A ~/_ ImFJQ�~E{PF �!��5� �")��{�� w5umvBu*�=,$&% j ~ 2 RJQ@:mC K(F#K(F#kJw ~+H<H�F��*�F�5x�{��!u K(F w ~ kJw ~+H<H<F��5�(��u/w!| A(B<FJLmK�FJL8FJL QWB<R?F#I(LmF#k;: ~FElLmF�K(Fkc~EB�~+kJQ 0JB<F?H5B<FJA(B<R?H<FJL Q�~EL Qowzy Fh4 A(B<F?H<HWMlC+L�B<RJ{fI(wOM10JB<F FJQ�B<FJQ<C+I(BWLmF I(LmF MOLmH<Q�~ELmk?F K(F��5�(��5u/w!| _ I(MB<FJA(B<R?H�FJL Q<F|w ~oD C+B@2 F3MOL Q<FJBWLmF|A C+I(B;wzy Fh4qA(B<F?H�HWMlC+L B<RJ{fI(wOM10JB<F %

75% ] j F�2 CqK�0JwlF|C/(5�WFJQ0K(F . AqQ@:mC+L FJQ)� ~cN+~ 7&-

�5% j ~L2 RJQ@:mCqK(F��*��5u/w K(F|w ~ kJw ~+H<H<F �5�(��u/w!| A(B<FJLmK I(LmF�k : ~FElLmF5K(F|kc~EB�~+kJQ 0JB<F?HvFJL ~EBW{fI�2 FJL QFJQ�B<FJQ<C+I(BWLmF�I(LmF3MOLmHWQ�~ELmk?F|K(F3w ~ kJw ~+H�H<F � �/w��!��u/w�_ I(M ~+H<H<CqkJMlF3wzy Fh4 A(B<F?H<HWMlC+L B<RJ{fI(wOM10JB<F�~EI Q<Fh4 Q<Fd ~EA(A ~EBWMlFJB %

75% j ~p2 RJQ@:mCqK(FLz�{F|!} K(F5w ~ kJw ~+H<H<F � �*��!��u/w Q<FJL Q<FoI(L#~EA(A ~EBWMlF32 FJL Q�K I Q<Fh4qQ<F A ~EB3wzy Fh4qA(B<F?H�HWMlC+LB<RJ{fI(wOM10JB<F FJQ�B<FJQ<C+I(BWLmF|NqB�~EM I(L Q<FJw�~EA(A ~EBWMlF32 FJL Q.Fh4 MlHWQ<FxFJQ�Dz~EI54 HWMOLmC+L %

]�% n M wzy ~EA(A ~EBWMlF32 FJL Q�K I Q<Fh4 Q<F5A ~EB.wzy Fh4 A(B<F?H<HWMlC+L B<RJ{fI(wOM10JB<F ~ B<RJImH<HWM � ~EwlC+B<HvwlF?H 2 RJQ@:mCqK(F?H+vmw'�()!xQ�~J�5�&w��|FJQ u/|B}xH�~ELmH�~EBW{fI�2 FJL Q<H � FJL QWB<F;~EI(QWB<F?H � K(F%w ~vkJw ~+H<H<F � �*��5u/wxA FJB@2 FJQWQ<FJL Q�K(F�B<R?kJI(A RJB<FJBB<F?H<A F?kJQWMONPF32 FJL Q0wlFvQ<Fh4qQ<F3B<F?k?C+L(L I A ~EB�wzy Fh4 A(B<F?H<HWMlC+L B<RJ{fI(wOM10JB<F|~EMOLmHWMO_ ImFvwlF?H MOLmK Mlk?F?H;K I K(R3((I(QFJQ.K(F3w ~ \mL K(Fxwzy ~EA(A ~EBWMlF32 FJL Q3Km~ELmH�wlFxQ<Fh4 Q<F %

p w)F?HWQ.A CfH<HWM'((wlF K(F�B<FJw ~ELmk?FJB3wzy ~EA(A ~EBWMlF32 FJL Q�FJL FJL NPCPA ~EL Q d LmC+I(NPFc~EI wlF=2 F?H<H�~E{PF z�{`|B} d wzy C/(5�WFJQ~EA(A ~EBWMlFJI(B %�[ wOQ<FJBWL ~EQWMONPF32 FJL Q�� w ~ 2 RJQ@:mC K(F ��(��!�5u5~�NPRJBWMy\ FxHWM wlF3Q<Fh4 Q<FxFJL QWMlFJB0F?HWQ;~EA(A ~EBWMlRxA ~EB�wzy Fh4B�A(B<F?H<HWMlC+L#B<RJ{fI(wOM10JB<F � k?C/2L2 F wzy Fh4qA(B<F?H<H<MlC+L#B<RJ{fI(wOM10JB<F ~?Nf~EMOQ|RJQ<R R?kJBWMOQ<FoA C+I(B�~EA(A ~EBWMlFJBxw ~ A CfHWMOQWMlC+L�K(FK(R3((I(Q0K(F|k;: ~FElLmF�~EI K(R3((I(Q0FJQ.K(F \mL K(Fxk : ~FElLmF d w ~ \mL �h%j ~ kJw ~+H<H<F � �(��5u&w K(Rh\mL(M�RJ{ ~EwlF32 FJL Q w ~�2 RJQ@:mC K(FLv�w �()!x � �()�|�� A C+I(BxB<R?kJI(A RJB<FJB|wlF5LmC/2=((B<F K(F

B<FJ{fB<C+I(A F32 FJL Q<H _ I(M.C+L Q RJQ<R ~EA(A ~EBWMlR?H ~EI H<FJMOL K(F wzy Fh4qA(B<F?H�HWMlC+L B<RJ{fI(wOM10JB<F ~EMOLmHWM�_ ImF w ~ 2 RJQ@:mCqK(Fvmw'�()!x�(9T -�A C+I(B;B<R?kJI(A RJB<FJB0wlF&T 032 F {fB<C+I(A F ~EA(A ~EBWMlR % j y MOLmK Mlk?F Z K(R?HWMO{fLmF|wlFx{fB<C+I(A F�k?C+BWB<F?H<A C+LmKm~EL Qd Q<C+I(Q<Fowzy Fh4 A(B<F?H<HWMlC+L�B<RJ{fI(wOM10JB<F � k?C/2L2 F HWM�k?FJwOwlFh� kJM%RJQ�~EMOQxQ<C+I/�[C+I(B<H FJL Q<C+I(B<R?F K(FoA ~EB<FJL Q@:�0?H<F?H �h% j F?H2 RJQ@:mCqK(F?H ~��5�&w�� (9T -�FJQ)u&|!}�(9T -3A FJB@2 FJQWQ<FJL Q;K(FvB<R?kJI(A RJB<FJB�B<F?HWA F?kJQWMONPF32 FJL Q;wlF?H MOLmK Mlk?F?H�K(F3K(R3((I(Q;FJQ\mL K(F3wzy ~EA(A ~EBWMlF32 FJL QvK IDT 032 F B<FJ{fB<C+I(A F32 FJL QvKm~ELmH�wzy Fh4 A(B<F?H<HWMlC+L B<RJ{fI(wOM10JB<F %j ~�\m{fI(B<F 75% � A(B<R?H<FJL Q<F w ~ NPFJB<HWMlC+L � ~cN+~ K(F wzy Fh4(F32 A(wlF#K(F k?C+L NPFJB<HWMlC+L K(F 2 C+L Q�~EL Q<H K y FJI(B<CfHd D B�~ELmk?H FJQ MOL NPFJB<H<F32 FJL Q K(R � d A(B<C+A CfH<R FJL . FJBWw % � L LmC+Q<F wlF?H K(FJI54 RJQ�~EA F?H K(F k?C/2 A(MOw ~EQWMlC+L8K(F

wzy Fh4 A(B<F?H<HWMlC+L�B<RJ{fI(wOM10JB<F�A C+I(B�kJB<R?FJB)I(LmF�MOLmHWQ�~ELmk?F�K(F�w ~0kJw ~+H<H<F �5�(��5u/w!|Q�?A(I(MlH�wzy ~+H<H<CqkJM ~EQWMlC+L d w ~;k;: ~FElLmFd ~EA(A ~EBWMlFJB�FJL kJB<Rc~EL Q I(LmF�MOLmHWQ�~ELmk?F�K(F � �*��5u/w.A ~EB wzy FJL NPC+MqK I*2 F?H<H�~E{PF��(��!��u/w d wzy C/(5�WFJQ �5�(��u/w!| %j ~ 2 RJQ@:mCqK(FNz�{`|!} F?HWQxI(QWMOwOMlH<R?F A C+I(B|A(B<Cqk?R?K(FJB d wzy ~EA(A ~EBWMlF32 FJL Q % t LmF5D C+MlH|wzy ~EA(A ~EBWMlF32 FJL Q5B<Rc~EwOMlH<R��Hcy MOw B<RJImH<HWMOQ��C+L I(QWMOwOMlH<F w ~ 2 RJQ@:mCqK(F vmw'�()�x (3{F|�� - A C+I(BoB<R?kJI(A RJB<FJB wlF Q<Fh4qQ<F ~EA(A ~EBWMlR Km~ELmH k;: ~+kJI(LK(F?H {fB<C+I(A F?H % � ~?Nf~�L y RJQ�~EL Q A ~+H HWA R?kJM ~EwlF32 FJL Q K(R?K MlR ~EI QWB�~EMOQ<F32 FJL Q K(F?H k : ~FElLmF?H K(F kc~EB�~+kJQ 0JB<F?H��kfy F?HWQ|H�~ELmH3HWI(BWA(BWMlH�FL_ ImFok?FJwOI(My� kJM%F?HWQ3I(LmFoA FJI A(wOImH|k?C/2 A(wlFh4 FL_ I y FJL . FJBWw � k?FL_ I(M�F?HWQ3NqMlHWM'((wlF Km~ELmHwzy ~EA(A ~EBWMOQWMlC+L K(F�k?C+L NPFJB<HWMlC+LmH.Fh4qA(wOMlkJMOQ<F?H.K(F|k : ~FElLmF d B<R?FJw %j y I(QWMOwOMlH�~EQWMlC+LoK(F�k?FJQWQ<F�kJw ~+H<H<F � ~?Nf~H�!~EA(B 0?H�k?C/2 A(MOw ~EQWMlC+L5K(F32 ~ELmK(F�K(F�A ~+H<H<FJB w ~;k : ~FElLmF%K I=2 C+L Q�~EL Qd QWB�~EMOQ<FJB.H<I(B�w ~5wOMO{fLmF|K(F|k?C/2L2 ~ELmK(F&,� �B�� /u�� &|��u/w�~B{(�&| �-� ��*�� u()�w'�B~H�

j ~ NPFJB<HWMlC+L . AqQ@:mC+L�K I 2��32 FoA(B<C+{fB�~�2L2 F ~EA(A ~EB�~FElQ d w ~�\m{fI(B<F 75%875% � I(QWB<FowlF?H|~+HWA F?kJQ<H3A(I(B<Fh�2 FJL QxH@AqL Q�~F4 M1_ ImF�K(F . A Q@:mC+L � wzy MOLmK(FJL Q�~EQWMlC+L�DG~EMlH�~EL Q.A ~EBWQWMlF MOL Q<RJ{fB�~EL Q<F K(F�w ~ H@AqL Q�~F4(F�FJQvw ~ DGC+B@2 FA ~EBWQWMlkJI(wOM10JB<F K(F5w ~ HWQWBWImkJQWI(B<F K(F k?C+L QWB��+wlF K y ~EwOQ<FJBWL ~EQWMONPF � � C+L B<F?k?C+L(L ~FElQ*((MlFJL#Km~ELmH3k?FJQ3Fh4(F32 A(wlFow ~wlRJ{m0JB<FJQ<RxH@AqL Q�~F4 M1_ ImFvK(F?H w ~EL({ ~E{PF?H�K(FvH<kJBWMOA(Q<H d w ~ . FJBWw�2 ~EMlH�~?NPF?k3I(L�2 C K�0JwlF3C/(5�WFJQ K I QWB�~EMOQ<F32 FJL QK(F?H5Fh4qA(B<F?H<H<MlC+LmH�B<RJ{fI(wOM10JB<F?H5HWM'2 MOw ~EMOB<F d k?FJwOI(M K(Fp� ~cN+~ % j y Fh4(R?kJI(QWMlC+L K y I(L A(B<C+{fB�~�2L2 F . A Q@:mC+L H<FDz~EMOQ;FJL ~EA(A FJw ~EL Q;w ~ k?C/2L2 ~ELmK(F,x�� &| ~?NPF?k|wlFxA(B<C+{fB�~�2L2 F d Fh4(R?kJI(Q<FJB0FJL A ~EB�~�2N0JQWB<F=,

� x�� /| �*�/|��u/w�~!{(�&| ��x�� |��!w5u � )!| � �/|��5�&|�� u(� )�|�u ��/|!|5�5{&u � �-� ��*�� u()�w'�B~

7&6 [ A(A(wOMlkc~EQWMlC+L K(F?H;Fh4 A(B<F?H<HWMlC+LmH;B<RJ{fI(wOM10JB<F?H

{ �5x �&w�� !��5��)��{��w5umvBu(�� 5�(��u/w!| �

{ �5x �&w�� !��5��)��{��w5umvBu(�� (��5u&w �

{ �5x �&w�� !��5��5u*�� u��{ �� /wm��*� �

x�) +��{�� !�B~�~ � �/|�5u&w�~!{*�/|�x�) +��5{!� ~��5�*��{!��'�5{�} ��{`|�( � �!w�{`|Bv � � �&w!v�~ - �� w�{`|Bv u(�!x�w�u&v � ( ��

�� -.( � � � � - ��

z ��!�(� � �&|��/|�� w�{`|Bv � �&|�|��5{/u �z ��!�(� | �*)�� /|��5�&|�� u5�!{ ��*� �/wm��(� }Bu*)�� {�z�z�w5uB~ � |5u($ � u5�!{ ��*� �/w&��(� ( � � � � � �- ��B�(��5u&w�| x � �5�(��5u/w!| �;�(�F�5x�{��u�( u(�!x�w5umv -�� (��!��u/w � � x��J��(��5u&w�(;�&w!v�~ �� -�

��w�� {�z ( �&� z�{`|B} ( -�- �

� �&|��5�&|�� ( |�uJ$ � ��(� ( �?��vmw'�()!x�( � -�- -��z��!�(��*)5u�( -�� &|�|5��{/u�� &� vmw �*)�x ( � -�{Fz ( ��/|!|5�5{&u�� u�� )��5~ ( D� �-�- �

|'�()� � �&|��/|�� o� �&|��5�&|�� z �� ~J�5uF�?�5�*)�� x�w�{`|��!�/| (@}Bu*)�� {�z�z�w5uB~H��z �/w&��(� ( | �*)�� /|��5�&|�� - �

u()�w'�B~H� �- �� u��B~mu �

|'�()� � �&|��/|�� o� �&|��5�&|�� z �� ~J�5uF�?�5�*)�� x�w�{`|��!�/| (@}Bu*)�� {�z�z�w5uB~H��z �/w&��(� ( | �*)�� /|��5�&|�� - �

�zmw5�&|��~>� �- �� u/|B} �mze{Fz ( -/u��B~mu

� u��5~&u �� ~��5u��&�1�()�� x!w�{`|��&|�( � 5~*�� &|�|5��{/u {`|��(�&|�|�)�u � ��&w!v�~ �� - �

� � � u&|!} �&ze{Fz ( -�u��5~&u� �&�(��!� ( � )&��+�u/w � �/wm��*� � ��/u&x��{*�/| u - �

� ��~��uF�?�5�()�� x�w�{F|��!�/|�( �&� vmw �*)�x ( � - � |�u w5u/x!w 5~&u/|��5u x5�5~ )�| | ��+�w�u�� - �

� � � u/|!} �mz �!w�� m�/�*�� u&|!} �&z ��{`| ( -

� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � ��!�B~!~&u � �&|��5u&w�~B{(�/|

�� 75% � � <�C+L NPFJB<H<MlC+L K(F+2 C+L(L ~EMlF|FJL � ~?Nf~

75% ] j F�2 CqK�0JwlF|C/(5�WFJQ0K(F . AqQ@:mC+L FJQ)� ~cN+~ 7mC

{ �5x �&w�� w5u � � �m} )��!u }BuB~ u*��x�w�uB~!~!{(�&|�~ w mv )��{ �&w5uB~u(�!x�w�u&v � w5u��;�(��Bx�{��u ( ��( ��

�� - ( � � � � - � -

�5{F|5u�� w5�($ �5{F|�x�)��( � � |��w�u��)�| ��/|��/|�� u*��)!|5u � �&|�|��5{/u � � -� � u(��x!w5umvB�J��(��!��(��5{F|5u -{Fz � �

� �/|��5�&|�� &��v�w �*)�x�( � -� �/|!|5��{/u�� &��v�w �*)�x�( � -{Fz � �&|�|5��{/u�� 1��

|'�()�� &|��5�&|�� z ��(� ( ��/|��/|�� - � � �� x!w�{`|�� (@| �*)�� /|��5�/|�� - � � � z u*)�w'�B~�� 5�&w�~ ( -

u��B~mu �|'�()�� &|��5�&|�� z ��(� ( ��/|��/|�� - � � �� x!w�{`|�� (@| �*)�� /|��5�/|�� - � � � z z�w5�&|��m~�� /w�~ ( -

u��5~&u �x�w�{F|�� B~ �� /|!|5��{/u {`|��(�/|!|�)�u � |B�

�� 75%87 � <�C+L NPFJB<HWMlC+L K(F�2 C+L(L ~EMlF�FJL . AqQ@:mC+L

7� [ A(A(wOMlkc~EQWMlC+L K(F?H;Fh4 A(B<F?H<HWMlC+LmH;B<RJ{fI(wOM10JB<F?H

� ��

� �� 8��

8� � ��

j ~ K(FJI54 M1032 F kc~EQ<RJ{PC+BWMlF K(F w ~EL({ ~E{PF?HxDGC+B@2 FJwlH�Km~ELmH|w ~ :(MlRJB�~EB<k :(MlF K(F�<>:mC/2 H@?BA F?HWQ k?C+LmHWQWMOQWImR?FK(F?H w ~EL({ ~E{PF?H K MOQ<H LmC+L5� k?C+L Q<Fh4 QWImFJwlH % n ~EI D�A C+I(B k?FJI54 _ I(M.H<C+L Q H<A R?kJMy\�_ ImF32 FJL Q B<RJ{fI(wOMlFJB<H � H<FJwlC+Lwzy MOLmkJwOImHWMlC+L K I Q@:mR?C+B 032 F � �mk?F?H�w ~EL({ ~E{PF?H�LmF3H<C+L Q�A ~+H�K(Rh\mL(MlH�H�~�((wlF?H A ~EB�K(F?H�Fh4qA(B<F?H<H<MlC+LmH B<RJ{fI(wOM10JB<F?H %t LmF0~EwOQ<FJBWL ~EQWMONPF0F?HWQ�k?FJA FJLmKm~EL Q�A(B<C+A CfH�R?F�A C+I(B�K(Rh\mL(MOB%k?F?H�w ~EL({ ~E{PF?H�FJL MOL Q<FJL QWMlC+L ,+wlF?H%{fB�~�2L2 ~EMOB<F?HLmC+L5� k?C+L Q<Fh4 QWImFJwOwlF?H % � A RJB�~EQWMlC+L(LmFJwOwlF32 FJL Q�� w ~ B<F?k?C+L(L ~EMlH�H�~ELmk?FoK(F?H0k : ~FElLmF?H.Dz~EMlH�~EL Q.A ~EBWQWMlF K y I(L w ~EL5�{ ~E{PFvLmC+L5� k?C+L Q<Fh4 QWImFJwlH;F?HWQ�B<Rc~EwOMlH�~�((wlFvA ~EB�I(L ~EI(Q<C/2 ~EQ<F d A(MOwlF % <�Fvk : ~EA(MOQWB<F3A(B<R?H�FJL Q<F3k?F?H K M0/ RJB<FJL Q<Hk?C+Lmk?FJA(Q<H %

�!�� -$! !�- �� 4�68= � =�� / � =.@ 4 %3@ 254�:<:<4�6. ~EB@2 M Q<C+ImH�wlF?H%w ~EL({ ~E{PF?H�k?C+LmH<QWBWI(MOQ<H�H<I(B%I(L ~EwOA�: ~�( FJQ K(C+L(LmR�� H<FJI(wlF;I(LmF.A FJQWMOQ<F.A ~EBWQWMlFvA FJI(Q �JQWB<F

K(Rh\mL(MlF d A ~EBWQWMOB|K y C+A RJB�~EQWMlC+LmHxFJLmH�F32,((wOMlHWQ<F?H|FJQxK(C+Lmk K y Fh4 A(B<F?H<HWMlC+LmH3B<RJ{fI(wOM10JB<F?HxQ<FJwOwlF?H+_ ImF5LmC+ImH3wlF?H~?NPC+LmH�NqI ~EI k : ~EA(MOQWB<F �5%!. C+I(B�k?FJI54p_ I(M LmF;D C+L Q�A ~+H�A ~EBWQWMlF0K(Fvk?FJQWQ<F0kJw ~+H�H<F0K(F?H�w ~EL({ ~E{PF?H�B<RJ{fI(wOMlFJB<H��wlF?H 2��32 F?H0A(B<C/((w1032 F?H�DGC+LmKm~�2 FJL Q�~EI54 H<F3A CfH<FJL Q.FJLmk?C+B<F�,

$&% <�C/2L2 FJL QvK(Rh\mL(MOB.k?F?H�w ~EL({ ~E{PF?H0FJL MOL Q<FJLmHWMlC+L��5% <�C/2L2 FJL QvK(R?kJMlK(FJB.HWM I(LmF|k : ~FElLmF ω ∈ Σ∗ ~EA(A ~EBWQWMlFJL Q3~EI w ~EL({ ~E{PF|C+I LmC+L��j ~vkc~EQ<RJ{PC+BWMlF�K(F?H�w ~EL({ ~E{PF?H�K MOQ<H)LmC+L5� k?C+L Q<Fh4qQWImFJwlH � C+I �F:mC+B<H � k?C+L Q<Fh4qQ<F?H�� F?HWQ�D C+B@2 R?F�K(F�w ~EL({ ~E{PF?H

K(C+L Qvw ~ HWQWBWImkJQWI(B<F5F?HWQ;Q<FJwOwlF=_ I y C+L A FJI(QvK(R?k?C+I(A FJBvH<F?H0k;: ~FElLmF?H3FJL A ~EBWQWMlF?H3K(C+L Q0w ~ HWQWBWImkJQWI(B<F�F?H<Q0w ~2��32 F A FJI�M'2 A C+BWQ<F wlF k?C+L Q<Fh4 Q<F Km~ELmH�wlF _ ImFJw�k?FJwOwlF?H@� kJM�~EA(A ~EB�~EMlH<H<FJL Q Km~ELmH�w ~ k : ~FElLmF�� d A ~EBWQWMOB K I2 C/2 FJL QvC$; FJwOwlF?H;H<C+L Q.~+K52 MlH<F?H;Km~ELmH.k?Fxk?C+L Q<Fh4 Q<F %j F?H w ~EL({ ~E{PF?H LmC+L5� k?C+L Q<Fh4 QWImFJwlH�H<C+L Q K(Rh\mL(MlH FJLxMOL Q<FJLmHWMlC+L d wzy ~EMlK(F%K(F�{fB�~�2L2 ~EMOB<F?H LmC+L5� k?C+L Q<Fh4qQWImFJwOwlF?H %

psL D C+B@2 FJwOwlF32 FJL Q��fI(LmF {fB�~�2L2 ~EMOB<F LmC+L5� k?C+L Q<Fh4 QWImFJwOwlF0F?HWQ I(L FJLmH<F32=((wlF;K(F�B 0J{fwlF?H�K(F�k?C+LmH<QWBWImkJQWMlC+L K(F?Hk : ~FElLmF?H.C+I A�:(B�~+H<F?H;K y I(L w ~EL({ ~E{PF %�. wOImH DGC+B@2 FJwOwlF32 FJL Q�� C+L w ~oK(Rh\mL(MOQ0K(F|w ~ 2 ~EL(M10JB<F�HWI(MONf~EL Q<F�,

�F��R��I"�� U��O�;lm��QMP��q�M`G��B " "� - I(LmF {fB�~�2L2 ~EMOB<F LmC+L5� k?C+L Q<Fh4 QWImFJwOwlF F?HWQ I(Lo_ I ~F�K BWI(A(wlFJQ G = (V, T, P, S) C$;V- F?HWQ;I(L FJLmH<F32=((wlF+\mL(M K(F3Nf~EBWM ~�((wlF?H0C+I LmC+L5�zQ<FJB@2 MOL ~EI54 �

T- F?HWQ�I(L FJLmH<F32,((wlF�\mL(M�K(FxQ<FJB@2 MOL ~EI54 � kfy F?HWQ � d � K MOB<F|wzy ~EwOA�: ~�( FJQ0K I w ~EL({ ~E{PF��

]�Z j ~EL({ ~E{PF?H;LmC+L5� k?C+L Q<Fh4 QWImFJwlH�� {fB�~�2L2 ~EMOB<F?H0FJQ.~EI(Q<C/2 ~EQ<F?H d A(MOwlF

P- F?HWQ I(L FJLmH�F32,((wlF \mL(M;K(F B 0J{fwlF?H K(F A(B<C K ImkJQWMlC+L K(F w ~ D C+B@2 F A → α C$; A F?HWQI(L H@A!2=( C+wlF LmC+L5�zQ<FJB@2 MOL ~EwvFJQ α F?HWQ I(LmF H<R _ ImFJLmk?F K(F H A!2=( C+wlF?H Q<FJB@2 MOL ~EI54 FJQLmC+L5�zQ<FJB@2 MOL ~EI54 �

S- F?HWQ I(L H@AB2,( C+wlFvLmC+L5�zQ<FJB@2 MOL ~Ew ~EA(A FJwlR 2 $T '$#&* d A ~EBWQWMOB;K I�_ ImFJw Q<C+I(Q<F?H wlF?H�k;: ~FElLmF?HK I w ~EL({ ~E{PF|H<C+L Q.FJL({PFJLmK B<R?F?H0A ~EB0~EA(A(wOMlkc~EQWMlC+L K(F?H;B 0J{fwlF?H;K(FxA(B<CqK ImkJQWMlC+L %

� qO�!�Rk� "� � �" � �!� ��qOkU��P�FIK�Q�� IKM� H�RE�MÌ �OGU�� ÌJ�Rk� "�� j F?H�B 0J{fwlF?H�K(F�A(B<CqK ImkJQWMlC+LoH<I(MON+~EL Q<F?HK(Rh\mL(MlH<H<FJL Q;I(LmFx{fB�~�2L2 ~EMOB<F�A C+I(B;wlF?H0Fh4qA(B<F?H<H<MlC+LmH0~EBWMOQ@:�2 RJQWM1_ ImF?H.HWM'2 A(wlF?H!,

E → E A E A→ �E → ( E - A→ �

E → � E A→ �E → {F} A→ �

A→�

j y ~F4 MlC/2 F K(F k?FJQWQ<F {fB�~�2L2 ~EMOB<F F?HWQ E MOLmkJwOImH�Km~ELmH wzy FJLmH<F32,((wlF V = {E,A} K(F?H|LmC+L5�zQ<FJB@2 MOL ~EI54 %j y FJLmH<F32=((wlF�K(F?H Q<FJB@2 MOL ~EI54 F?HWQ T = { ( , - , {F} , � , � , � , � ,�}% j C+B<H _ ImF�A(wOImH<MlFJI(B<H B 0J{fwlF?H�K(F�A(B<CqK ImkJQWMlC+L

Hcy ~EA(A(wOM1_ ImFJL Q3~EI 2��32 F|H@AB2,( C+wlF|LmC+L5�zQ<FJB@2 MOL ~Ew � C+L I(QWMOwOMlH<F|{PRJLmRJB�~EwlF32 FJL Q3I(LmF3DGC+B@2 F ~�((B<RJ{PR?F ~cNPF?kw ~5NPFJBWQWMlkc~EwlF�K y ~EwOQ<FJBWL ~EQWMONPF=,

E → E A E | ( E - | � E | {�}A → � | � | � | � | �

2

j y ~EA(A(wOMlkc~EQWMlC+L�K(F?HvB 0J{fwlF?H3K(F A(B<CqK ImkJQWMlC+L A FJB@2 FJQxK(F {PRJLmRJB<FJB3wlF?H.A�:(B�~+H�F?HvK I w ~EL({ ~E{PF % <vy F?HWQ3w ~LmC+QWMlC+L K(F|K(RJBWMONf~EQWMlC+L ,

� E!��I ��5MÌ"�� - � LmC+Q<R?F ⇒ � ~EA(A(wOMlkc~EQWMlC+L K y I(L B 0J{fwlF5K(F|A(B<CqK ImkJQWMlC+L A C+I(B.B<F32 A(w ~+k?FJB.I(LLmC+L5�zQ<FJB@2 MOL ~Ew)A ~EB�wzy I(LmF|K(F?H0A ~EBWQWMlF?H;K B<C+MOQ<F?H0K(F|H�F?H B 0J{fwlF?H0K(FxA(B<CqK ImkJQWMlC+L %

� qO�!�Rk� "� � �1D c ~ELmH yE yW� C+L A FJI(Q.B<F32 A(w ~+k?FJBxwlF|LmC+L5�zQ<FJB@2 MOL ~Ew E FJL I(QWMOwOMlH�~EL Q3w ~ QWB<C+MlHWM1032 F B 0J{fwlFK(F A(B<CqK ImkJQWMlC+L'K(F w ~ {fB�~�2L2 ~EMOB<F A(B<R?k?R?K(FJL Q<F A C+I(B5C/((Q<FJL(MOB�� E �)k?Fp_ ImF wzy C+L LmC+Q<F E ⇒ � E

%� L A FJI(Q ~EA(A(wOM1_ ImFJB d LmC+I(NPFc~EI I(LmF K(RJBWMONf~EQWMlC+L FJQ ~EMOLmH<M0K(F HWI(MOQ<F k?C/2L2 F Km~ELmH w ~#H<R _ ImFJLmk?F K(FK(RJBWMONf~EQWMlC+LmH0HWI(MONf~EL Q<F�,

E ⇒ � E ⇒ � ( E - ⇒ � ( E A E - ⇒ � (b{�} A E - ⇒ � ( {F} � E -

⇒ � ( {F} � {�} - 2

X L Q<FJB@2 F?H0K(FvNPCqkc~�((I(w ~EMOB<F|FJQ;K(F3LmC+Q�~EQWMlC+LmH��mC+L K MOB�~ _ ImF E H<F3K(RJBWMONPF|FJL � E LmC+Q<R E ⇒ � E%

j y ~EA(A(wOMlkc~EQWMlC+L K(F Z � $ � C+I�A(wOImHWMlFJI(B<H�K(RJBWMONf~EQWMlC+LmH H�FoLmC+Q<F ∗⇒% � L�A C+I(BWB�~ K(C+Lmk R?kJBWMOB<Fp_ ImF E

∗⇒

� ( {F} � {�} - % j C+B<H _ I y ~EIp2 C+MOLmH�I(LmF0K(RJBWMONf~EQWMlC+L F?HWQ�Dz~EMOQ<F�� C+L I(QWMOwOMlH<FJB�~xw ~3LmC+Q�~EQWMlC+L +⇒ _ I(MmB�~EA(A FJwOwlF

w ~ DGFJB@2 FJQWI(B<F A CfH<MOQWMONPF A ~EB B�~EA(A C+BWQ d w ~ D FJB@2 FJQWI(B<F K(F �3wlF?FJLmF Km~ELmH wlF?H Fh4 A(B<F?H<HWMlC+LmH B<RJ{fI(wOM10JB<F?H %[ MOLmHWM � C+L ~ E

+⇒ � ( {F} � {F} - % � L MOL QWB<C K I(MOQ RJ{ ~EwlF32 FJL Q�wlF?H�LmC+QWMlC+LmH K(F 3��('�8 '�3Q4 � 2$ *xFJQJ354 �(2 �* ,

� �F��MP��k! ��P��- H�R _ ImFJLmk?F K(F H@A!2=( C+wlF?HoQ<FJB@2 MOL ~EI54 FJQ LmC+L5�zQ<FJB@2 MOL ~EI54'C/((Q<FJL ImF A ~EBK(RJBWMONf~EQWMlC+L d A ~EBWQWMOB.K(Fxwzy ~F4qMlC/2 F %

]�%'$=� B�~�2L2 ~EMOB<F?H0LmC+L5� k?C+L Q<Fh4 QWImFJwOwlF?H ]�$

� ��P��- H<R _ ImFJLmk?F#K(F H@AB2,( C+wlF?H Q<FJB@2 MOL ~EI54�C/((Q<FJL ImF#A ~EB K(RJBWMON+~EQWMlC+L d A ~EBWQWMOB K(Fwzy ~F4 MlC/2 F %

j F?H LmC+QWMlC+LmH�K(F.K(RJBWMONf~EQWMlC+LM�(K(FvA(B<C+Q<C+A�:(B�~+H<FxFJQ K(F.A�:(B�~+H�F.LmC+ImH�~�2N0JLmFJL Q d K(Rh\mL(MOB�w ~�LmC+QWMlC+L K(Fw ~EL({ ~E{PF|K(Rh\mL(M�A ~EB�I(LmFx{fB�~�2L2 ~EMOB<F&,

� ��lmlm��kUMPEpkH��,GH��L��F��R��I"��G- nqC+MOQ G = (V, T, P, S) I(LmF {fB�~�2L2 ~EMOB<FLmC+L5� k?C+L Q<Fh4qQWImFJwOwlF�� wlFvw ~EL({ ~E{PFxK(Rh\mL(M A ~EB�k?FJQWQ<F3{fB�~�2L2 ~EMOB<F�� LmC+Q<R L(G) � F?HWQ wzy FJLmH<F32=((wlFK(F?H;A�:(B�~+H<F?H ω ∈ T ∗ Q<FJwOwlF?H _ ImF S

+⇒ ω

%

� UE��FrB�R� � �J�� @&)W2$@ 2� * L(G) �6R �J@�T 3H2 � �@B* �� 2$# #�2$T �(*�@Q'$@ � <P'$@Q8S* �8 ��*>) )+* G *> >8 �@=)W2$@62�6*@Q'$@ � <P'$@Q8S* �8 ��*>) �<�C/2L2 F LmC+ImH wzy ~cNPC+LmH B�~EA(A FJwlR FJL K(R3((I(Q#K(F k;: ~EA(MOQWB<F��3MOw H<F�A CfH<F A C+I(B wlF?H w ~EL({ ~E{PF?H LmC+L5�

k?C+L Q<Fh4 QWImFJwlH�wlF?H�2��32 F?HO_ ImF?HWQWMlC+LmH DGC+LmKm~�2 FJL Q�~EwlF?HH_ ImF A C+I(B Q<C+ImH wlF?H w ~EL({ ~E{PF?H DGC+B@2 FJwlH % f C+ImH NPFJLmC+LmHK(F NPC+MOB|k?C/2L2 FJL Q5K(Rh\mL(MOB�FJL�MOL Q<FJLmHWMlC+L�I(L�w ~EL({ ~E{PF LmC+L5� k?C+L Q<Fh4 QWImFJw�FJL�I(QWMOwOMlH�~EL Q|I(LmF {fB�~�2L2 ~EMOB<FLmC+L5� k?C+L Q<Fh4 QWImFJwOwlF % <�C/2L2 FJL Q;NPRJBWMy\ FJB _ I y I(LmFvA�:(B�~+H<Fx~EA(A ~EBWQWMlFJL Q d L(G) � . C+I(B;k?FJw ~H� MOw Dz~EI(Q�QWB<C+I5�NPFJBxI(LmF H<R _ ImFJLmk?F K(FoK(RJBWMON+~EQWMlC+LmH K(F w ~ A�:(B�~+H�F K(FJA(I(MlHxwzy ~F4qMlC/2 F K(F G

%�. FJLmKm~EL Q5k?FoA(B<C k?F?H�HWImH�� dk : ~/_ ImF�~EA(A(wOMlkc~EQWMlC+L K y I(LmF|K(RJBWMON+~EQWMlC+L M'2 A(wOM1_ ImF�K(FJI54 k;:mC+My4 Hcy M'2 A CfH�FJL Q!,$&% � ImFJw LmC+L5�zQ<FJB@2 MOL ~Ew�B<R?K I(MOB<F �

�5% � ImFJwOwlF�B 0J{fwlFxK(FxA(B<CqK ImkJQWMlC+L I(QWMOwOMlH<FJB�A C+I(B;B<R?K I(MOB<FxwlFxLmC+L5�zQ<FJB@2 MOL ~Ew)k :mC+MlHWM �X L�Dz~EMOQ�� Km~ELmH|I(LmF A(B<C+Q<C+A�:(B�~+H<F��MOw A�~ H<C+I(NPFJL Q A(wOImHWMlFJI(B<H LmC+L5�zQ<FJB@2 MOL ~EI54 kc~ELmK MlKm~EQ<H d w ~ B<Rh�

K ImkJQWMlC+L % a C+ImHvA FJI(NPFJL QvRJ{ ~EwlF32 FJL Q �JQWB<F�k :mC+MlH<MlH0A C+I(B.F>/ F?kJQWImFJB.w ~ K(RJBWMON+~EQWMlC+L % psw H<F|QWB<C+I(NPF _ I y MOw)~RJQ<R0K(R32 C+L QWB<R�_ ImF.k?F0k :mC+My4 L y MOLHOmImFJLmk?FvA ~+H�wlF�Dz~EMOQ�K(F0QWB<C+I(NPFJB�C+I LmC+L I(LmF0H�R _ ImFJLmk?FvK(F0K(RJBWMONf~EQWMlC+LA FJB@2 FJQWQ�~EL Q;K y FJL({PFJLmK B<FJB;I(LmFvA�:(B�~+H<F % j F3k :mC+My4 K I LmC+L5�zQ<FJB@2 MOL ~Ew H<F0DG~EMOQ�K(C+Lmk3H<FJwlC+L I(LmF3HWQWB�~EQ<RJ{fMlFd K(RJQ<FJB@2 MOLmFJB % j F?H0K(FJI54 HWQWB�~EQ<RJ{fMlF?H;wlF?H�A(wOImH0I(QWMOwOMlH<R?F?H;H<C+L Q!,� w ~ K(RJBWMONf~EQWMlC+L d { ~EImk :mF�� LmC+Q<R?F ⇒

g

C$; C+L k :mC+MlH<MOQ.Q<C+I/�WC+I(B<HvwlF|LmC+L5�zQ<FJB@2 MOL ~Ew wlF|A(wOImH d { ~EImk;:mFKm~ELmH�w ~oA(B<C+Q<C+A�:(B�~+H<F�� FJQ

� w ~ K(RJBWMONf~EQWMlC+L d K B<C+MOQ<F�� LmC+Q<R?F ⇒d

C$; C+L k :mC+MlHWMOQ5Q<C+I/�[C+I(B<H wlF LmC+L5�zQ<FJB@2 MOL ~Ew wlF A(wOImH d K B<C+MOQ<FKm~ELmH�w ~oA(B<C+Q<C+A�:(B�~+H<F %. C+I(B0k?C/2 A(B<FJLmK B<F�FJQ 2 ~EL(MOA(I(wlFJB0wlF?H�K(RJBWMON+~EQWMlC+LmH�� MOw F?HWQ�H<C+I(NPFJL Q�I(QWMOwlFxK(F3A ~+H<H<FJB A ~EB I(LmF3B<FJA(B<Rh�

H<FJL Q�~EQWMlC+L {fB�~EA�:(M1_ ImF��(A(wOImH;A(B<R?kJMlH<R32 FJL Q0I(L ~EB@((B<F|K(F�K(RJBWMON+~EQWMlC+L ,j�� U�� nU� nHE��/I ��5M`I"�� - j y ~EB@((B<F5K(F K(RJBWMONf~EQWMlC+L#K y I(LmF�A�:(B�~+H<F5F?HWQvC/((Q<FJL I#K y I(LmF K(Rh�BWMONf~EQWMlC+L A ⇒ α1 ⇒ α2 . . . ⇒ αn

K(F|w ~ 2 ~EL(M10JB<F�HWI(MONf~EL Q<F�,� j ~oB�~+kJMOLmF|K(F3wzy ~EB@((B<F K(FxK(RJBWMON+~EQWMlC+L F?HWQ A

%� nqC+MOQxI(LmF A(B<C+Q<C+A�:(B�~+H�F αi = X1 . . . Xj . . . Xk

FJQ Xj → Xj1 . . . Xjm

w ~ B 0J{fwlF5K(FA(B<C K ImkJQWMlC+L ~EA(A(wOM1_ ImR?F A C+I(B�C/((Q<FJL(MOB αi+1

�+~EwlC+B<H wzy ~EB@((B<F�K(F K(RJBWMONf~EQWMlC+L d wzy RJQ�~EA F i+1F?HWQ;C/((Q<FJL I K(F3wzy ~EB@((B<F d wzy RJQ�~EA F i FJL ~F�WC+I(Q�~EL Q m \mwlH Xj1 . . . Xjm

d w ~ DGFJI(MOwOwlF Xj%

� qO�!�Rk� "� � �'i <�C+LmHWQWBWI(MlH<C+LmH�wzy ~EB@((B<F A C+I(Bxw ~ H<R _ ImFJLmk?F K(F K(RJBWMON+~EQWMlC+LmH�A(B<R?k?R?K(FJL Q<F K(F w ~ A�:(B�~+H<F�.( {F} � {F} - % nqFJwlC+L w ~ A(B<F32 M10JB<F B 0J{fwlF��w ~ B�~+kJMOLmF K(F wzy ~EB@((B<F F?HWQ E

% j y ~EA(A(wOMlkc~EQWMlC+L K(F w ~#A(B<F32 M10JB<FK(RJBWMONf~EQWMlC+L E ⇒ � E LmC+ImH.K(C+L(LmFxwzy ~EB@((B<F�,

E@@

@@

��

�E

] � j ~EL({ ~E{PF?H;LmC+L5� k?C+L Q<Fh4 QWImFJwlH�� {fB�~�2L2 ~EMOB<F?H0FJQ.~EI(Q<C/2 ~EQ<F?H d A(MOwlF

j ~oQWB<C+MlHWM1032 F|RJQ�~EA F|K(FxK(RJBWMONf~EQWMlC+L � E ⇒ � ( E - k?C+LmHWQWBWI(MOQ0wlF?H \mwlH;K(F3w ~5DGFJI(MOwOwlF E ,

E@@

@@

��

�E

>>>>

~~~~

( E -

� w ~ _ I ~EQWBWM1032 F�RJQ�~EA F�� ( E - ⇒ � ( E A E - �(C+L A ~+H<H<F d ,

E@@

@@

��

�E

@@@@

~~~~

( E@@

@@

~~~~

-

E A E

j F?H QWB<C+MlH RJQ�~EA F?H HWI(MONf~EL Q<F?H�� ( E A E - ⇒ � ( {�} A E - ⇒ � ( {�} � E - ⇒� ( {F} � {�} -6�qDGC+L Qv~EA(A ~EB�~FElQWB<F|wlF?H�QWB<C+MlH;D FJI(MOwOwlF?H;K(F�H@A!2=( C+wlF?H;Q<FJB@2 MOL ~EI54.,

EBB

BB

~~~~

�E

AAAA

A

}}}}

}

( EAA

AA

}}}}

-

E A E

{�} � {�}2

� w ~ _ ImF?HWQWMlC+L K(F3H�~?NPC+MOB �&<�C/2L2 FJL Q0K(R?kJMlK(FJB�HWM I(LmFvA�:(B�~+H<F ω ∈ L(G) � ��(C+L B<RJA C+LmK�_ I y MOw DG~EI(QQWB<C+I(NPFJB�I(LmF K(RJBWMONf~EQWMlC+L d A ~EBWQWMOB5K(Fowzy ~F4qMlC/2 F K(Fow ~ {fB�~�2L2 ~EMOB<F G C+I�~EwlC+B<H�k?C+LmHWQWBWI(MOB<F I(L ~EB@((B<FK(F|K(RJBWMONf~EQWMlC+LM� ~EImH<HWM ~EA(A FJwlR�~EB@((B<F|K y ~EL ~Ew'A H<F��(A C+I(B0k?FJQWQ<FxA�:(B�~+H�F %�. ~EB@2 M�wlF?H0~EA(A(wOMlkc~EQWMlC+LmH.wlF?H�A(wOImHM'2 A C+BWQ�~EL Q<F?H)K(F?H {fB�~�2L2 ~EMOB<F?H�LmC+L5� k?C+L Q<Fh4 QWImFJwOwlF?H)H�F�QWB<C+I(NPF�w ~�K(Rh\mL(MOQWMlC+L5K(F�w ~�H@AqL Q�~F4(F�K(F?H w ~EL({ ~E{PF?HK(F A(B<C+{fB�~�2L2 ~EQWMlC+L % j ~ A ~EBWQWMlF K I k?C/2 A(MOw ~EQ<FJI(BN_ I(M�H<F k : ~EBW{PF K(F NPRJBWMy\ FJBoHWM�I(L�A(B<C+{fB�~�2L2 F F?HWQk?C+L DGC+B@2 F d w ~ H@A L Q�~F4 F5K I w ~EL({ ~E{PF�Dz~EMOQ3Fh4(~+kJQ<F32 FJL Q|k?FJw ~ , MOw)k?C+LmH<QWBWI(MOQvI(L�~EB@((B<F5K y ~EL ~Ew'AqH�F A C+I(BwlF3A(B<C+{fB�~�2L2 F�� ~EB@((B<F+_ I(M H<FJBWQ�LmC+L H<FJI(wlF32 FJL Q d 2 C+L QWB<FJB�_ ImF3wlF3A(B<C+{fB�~�2L2 F F?HWQ�H@AqL Q�~F4 M1_ ImF32 FJL Qk?C+BWB<F?kJQ��2 ~EMlH.H<FJBWQ0~EImH<HWM K(F+( ~+H�F|~EI54 QWB�~EMOQ<F32 FJL Q<HvH<I�(mH<R _ ImFJL Q<H�B<Rc~EwOMlH<R?H0A ~EB�wlF|k?C/2 A(MOw ~EQ<FJI(B %

�!�� 2|@ � !�- @ 4�� :�4

j y ~EI(Q<C/2 ~EQ<F d A(MOwlF|F?HWQ.~EI54 {fB�~�2L2 ~EMOB<F?H.LmC+L5� k?C+L Q<Fh4 QWImFJwOwlF?Hvk?F,_ ImFxwlF?H.~EI(Q<C/2 ~EQ<F?H.K y RJQ�~EQ<H�\mL(MlHH<C+L Qx~EI54 Fh4qA(B<F?H�HWMlC+LmHvB<RJ{fI(wOM10JB<F?H % p L DGC+B@2 FJwOwlF32 FJL Q�� I(L#~EI(Q<C/2 ~EQ<F d A(MOwlFoF?HWQvI(L�~EI(Q<C/2 ~EQ<F K y RJQ�~EQ<H\mL(M�~EI�_ ImFJw F?HWQ0~+K��WC+MOL Q;I(LmF|A(MOwlF %�. wOImH DGC+B@2 FJwOwlF32 FJL Q�� MOw F?HWQ;K(Rh\mL(M K(Fxw ~ 2 ~EL(M10JB<F HWI(MONf~EL Q<F�,

j�G�MP��R�5MP�=�=k�IJ "� - I(L5~EI(Q<C/2 ~EQ<F d A(MOwlF�F?HWQ I(LmF�H<QWBWImkJQWI(B<F AP = (Q,Σ,Γ, δ, q0, Z0, F )C$;N,

]�% �L[ I(Q<C/2 ~EQ<F d A(MOwlF ]�7

Q F?HWQ�I(L FJLmH<F32=((wlF+\mL(M K y RJQ�~EQ<H %Σ F?H<Q;wzy ~EwOA�: ~�( FJQ)\mL(M K y FJL QWB<R?F %Γ F?HWQ�wzy ~EwOA�: ~�( FJQ \mL(M K(F3A(MOwlF %δ F?HWQ�I(LmFoD C+LmkJQWMlC+L K(F QWB�~ELmHWMOQWMlC+L K(FJA(I(MlH Q × Σ ∪ {ε} × Γ NPFJB<H�wlF?H�H<C+ImH � FJLmH�F32,((wlF?H

\mL(MlH.K(F Q× Γ∗%

q0 ∈ Q F?HWQ�wzy RJQ�~EQ;MOL(MOQWM ~Ew %Z0 ∈ Γ F?HWQ�wlF�H@A!2=( C+wlF3A(w ~+k?R|MOL(MOQWM ~EwlF32 FJL Q3Km~ELmH�w ~oA(MOwlF %F ⊆ Q F?HWQ�wlFxH<C+ImH@� FJLmH<F32,((wlF K(F?H;RJQ�~EQ<H \mL ~EI54 %

j ~ D C+LmkJQWMlC+L�K(F QWB�~ELmHWMOQWMlC+L�F?HWQ3I(QWMOwOMlH<R?FoK(F5w ~N2 ~EL(M10JB<F H<I(MON+~EL Q<F % t L H@AB2,( C+wlF5F?H<QvK(RJA(MOwlR FJQ3I(LH@AB2,( C+wlF K(F wzy FJL QWB<R?F F?H<Q k?C+LmH<C/2L2 R C+I I(L ε �zQWB�~ELmHWMOQWMlC+L F?HWQ K(R?kJwlFJLmk;:mR?F FJQ wzy ~EI(Q<C/2 ~EQ<F F>/ F?kJQWImFI(LmF QWB�~ELmHWMOQWMlC+L NPFJB<H.I(L K(F?HvRJQ�~EQ<HvH<A R?kJMy\ R?HvA ~EBvw ~ DGC+LmkJQWMlC+L K(F QWB�~ELmHWMOQWMlC+LM� A(I(MlH Z � $ C+I A(wOImH<MlFJI(B<HH@AB2,( C+wlF?H;RJ{ ~EwlF32 FJL Q3HWA R?kJMy\ R?H�A ~EB�w ~5DGC+LmkJQWMlC+L K(F3QWB�~ELmHWMOQWMlC+L H<C+L Q0F32 A(MOwlR?H %

�,�Q�Rk ��`MP�B�R�B�QM*nJI'��lmlm�!k�MP�5M`I"�Q� - wlF0k?C/2 A C+BWQ<F32 FJL Q�K y ~+k?k?FJA(Q�~EQWMlC+L K y I(L ~EI(Q<C/2 ~EQ<Fd A(MOwlF AP k?C+LmHWMlH<Q<F d k?C+LmH�C/2L2 FJB.Q<C+I(Q<F�w ~ k : ~FElLmF5K y FJL QWB<R?F ω FJQ d A ~EBWNPFJL(MOBvKm~ELmH.I(LRJQ�~EQb\mL ~Ew f ∈ F ~EwlC+B<H)_ ImFvw ~5A(MOwlFxK(Fvwzy ~EI(Q<C/2 ~EQ<F|F?HWQ�NqMlK(F � w ~ok;: ~FElLmF ω F?HWQ;~EwlC+B<H;K MOQ<F~+k?k?FJA(Q<R?F�A ~EB;wzy ~EI(Q<C/2 ~EQ<F AP

%<�C/2L2 F A C+I(B|wlF?H ~EI(Q<C/2 ~EQ<F?H5K y RJQ�~EQ<H+\mL(MlH�� wlF k?C/2 A C+BWQ<F32 FJL QoK y ~+k?k?FJA(Q�~EQWMlC+L K(F wzy ~EI(Q<C/2 ~EQ<F d

A(MOwlFxLmC+ImH0~�2N0JLmF d K(Rh\mL(MOB;w ~oLmC+QWMlC+L K(F3w ~EL({ ~E{PF5~+k?k?FJA(Q<RxA ~EB;I(L ~EI(Q<C/2 ~EQ<F d A(MOwlF ,� �� lmlm�!k�MPE kH�� GH� ��G�MP��5MP��ok�IJ "� - nqC+MOQ AP = (Q,Σ,Γ, δ, q0, Z0, F )I(L�~EI(Q<C/2 ~EQ<F d A(MOwlF�� ~EwlC+B<H|wlF w ~EL({ ~E{PF ~+k?k?FJA(Q<RoA ~EB AP � LmC+Q<R L(AP ) F?HWQ3wzy FJLmH<F32,((wlFK(F?H0k : ~FElLmF?H ω ∈ Σ∗ Q<FJwOwlF*_ ImF ω F?H<Q0~+k?k?FJA(Q<R?F|A ~EB AP

%<�F _ I(M LmC+ImH3A FJB@2 FJQ|K y RJLmC+Lmk?FJBxwlFoQ@:mR?C+B 032 F K y R _ I(MONf~EwlFJLmk?F FJL QWB<FowlF?H|~EI(Q<C/2 ~EQ<F?H d A(MOwlF FJQ3wlF?H

{fB�~�2L2 ~EMOB<F?H.LmC+L5� k?C+L Q<Fh4 QWImFJwOwlF?H�,� UE��FrB�R� � � D � R�� T �F2�)W*>@B<7* �(2$# #�2$T �(*!@Q'$@ � <P'$@Q8S* �8 ��*>) )+* � 2 �8 '$#�2�8S* � 3BT )+* � �B'$TU8 G � @ * �� 2$# �#�2$T �(*�@Q'�@ � <P'�@58S* �8 ��*>)A)W* �6R � @�T 7 2$@58 )W*�)W2$@62�6* L(G) � 2$)W' �� !T ) * $T >8S* �@D2 �8 '�# 2 8S* � 3QTA)W* AP 8S*9)� ��* L(AP ) = L(G) *98 �PR(<9T 3��(' � ��*>#&*>@58 �j F A(B<C/((w1032 F�_ I(M�Nf~�2 ~EMOL Q<FJL ~EL Q H<F A CfH<FJB�� k?C/2L2 F MOw%Hay F?HWQ|A CfH<RoA C+I(B wlF?H�~EI(Q<C/2 ~EQ<F?H5K y RJQ�~EQ<H

\mL(MlH5A ~EBoB�~EA(A C+BWQ ~EI54 Fh4 A(B<F?H<HWMlC+LmH5B<RJ{fI(wOM10JB<F?H�� F?HWQoK(F H�~cNPC+MOB k?C/2L2 FJL Q k?C+LmHWQWBWI(MOB<F wzy ~EI(Q<C/2 ~EQ<F dA(MOwlF B<F?k?C+L(L ~EMlH<H�~EL Q wlF w ~EL({ ~E{PF K(Rh\mL(M A ~EB I(LmF {fB�~�2L2 ~EMOB<F LmC+L5� k?C+L Q<Fh4 QWImFJwOwlF G

% t L ~EI(Q<C/2 ~EQ<F dA(MOwlF ~EL ~Ew'AqH<FJI(BoA C+I(B I(LmF {fB�~�2L2 ~EMOB<F LmC+L5� k?C+L Q<Fh4 QWImFJwOwlF K(Rh\mL(MOQoI(LmF A(B<C k?R?K I(B<F A ~EBow ~/_ ImFJwOwlF I(LmFK(RJBWMONf~EQWMlC+L C+I I(L'~EB@((B<F K y ~EL ~Ew'A H<F H<FJB<C+L Q k?C+LmHWQWBWI(MOQ<H5A C+I(B I(LmF A�:(B�~+H<F K(F�2 ~EL(M10JB<F d NPRJBWMy\ FJB HWMk?FJwOwlFh� kJM ~EA(A ~EBWQWMlFJL Q ~EI w ~EL({ ~E{PF0K(Rh\mL(MmA ~EB�w ~3{fB�~�2L2 ~EMOB<F %!. wOImHWMlFJI(B<H%K M0G kJI(wOQ<R?H�H<F A CfH<FJL Q % c y ~�( C+B<K �wlF5k :mC+My4 K(F5w ~ B 0J{fwlFoK(F�A(B<CqK ImkJQWMlC+L d ~EA(A(wOM1_ ImFJB d k;: ~/_ ImFoRJQ�~EA FoK(F K(RJBWMONf~EQWMlC+L A FJI(Q3MOLmK I(MOB<FoK(F?HR?k :mF?k?H�Km~ELmH�w ~ k?C+LmHWQWBWImkJQWMlC+L K(F0w ~ K(RJBWMONf~EQWMlC+L % t LmFvHWQWB�~EQ<RJ{fMlF3K(F.k?C+LmHWQWBWImkJQWMlC+L K(Fvw ~ K(RJBWMON+~EQWMlC+L C+IK(F wzy ~EB@((B<F K(C+MOQ ~EImH<HWM �JQWB<F k :mC+MlHWMlF ,�A ~EBWQWMOB K(F wzy ~F4qMlC/2 F A C+I(Bo~EwOwlFJB NPFJB<H w ~ A�:(B�~+H�F C+I wzy MOL NPFJB<H<F �c M0/ RJB<FJL Q<F?HvD C+B@2 F?HxK(F {fB�~�2L2 ~EMOB<F?H|H<C+L Q�2 MlFJI54 ~+Km~EA(Q<R?F?H d wzy I(LmFoC+I d wzy ~EI(QWB<FoK(Fok?F?HvH<QWB�~EQ<RJ{fMlF?H %X L5\mLM�(w ~ A FJB[DGC+B@2 ~ELmk?F|K(F?H0~EL ~Ew'A H<FJI(B<H0F?H<Q�I(L A C+MOL Q0kJBWImkJM ~Ew A C+I(B�wlF?H0~EA(A(wOMlkc~EQWMlC+LmH %p w)Fh4qMlHWQ<F�FJL Dz~EMOQ0A(wOImHWMlFJI(B<H 2 RJQ@:mC K(F?HvA C+I(B.k?C+LmHWQWBWI(MOB<F5K(F?H.~EL ~Ew'A H<FJI(B<H % <�FJBWQ�~EMOLmF?HvH<C+L QvI(L(MONPFJB �

H<FJwOwlF?H��~EI�H<FJLmH|C$;�FJwOwlF?H Hcy ~EA(A(wOM1_ ImFJL Q d Q<C+I(Q<F?H wlF?Hx{fB�~�2L2 ~EMOB<F?H LmC+L5� k?C+L Q<Fh4 QWImFJwOwlF?H % j F K(RiDz~EI(Q K(Fk?F?HL2 RJQ@:mCqK(F?H F?HWQL_ I y FJwOwlF?H LmF A(B<C K I(MlH�FJL Q A ~+H K(F?H ~EL ~Ew'A H<FJI(B<H F>G kc~+k?F?H � Q<F32 AmH K y ~EL ~Ew'A H<F Km~ELmH0(n3) C$; n F?HWQ w ~ Q�~EMOwOwlFvK(Fvw ~�A�:(B�~+H<F d ~EL ~Ew'AqH<FJB �h% c y ~EI(QWB<F?Hb2 RJQ@:mCqK(F?H A(B<C K I(MlH<FJL Q;K(F?H;~EL ~Ew'AqH�FJI(B<HF>G kc~+k?F?H��t2 ~EMlH|FJwOwlF?H3LmF H�C+L QxA ~+H3I(L(MONPFJB<H<FJwOwlF?H %�. C+I(BWQ�~EL Q�wlF?HxkJw ~+H<H<F?HxK(Fo{fB�~�2L2 ~EMOB<F?H|QWB�~EMOQ<R?F?HxA ~EB

]&] j ~EL({ ~E{PF?H;LmC+L5� k?C+L Q<Fh4 QWImFJwlH�� {fB�~�2L2 ~EMOB<F?H0FJQ.~EI(Q<C/2 ~EQ<F?H d A(MOwlF

k?F?H+2 RJQ@:mCqK(F?H�H<C+L Q�H<C+I(NPFJL Q|B<FJw ~EQWMONPF32 FJL Q5BWMlk :mF?H��FJQ|HWIHG H�~EL Q<F?H�Km~ELmHxwlF?H5~EA(A(wOMlkc~EQWMlC+LmH|A(B�~EQWM1_ ImF?H� k?C/2L2 F A ~EBvFh4(F32 A(wlF K(Rh\mL(MOBvw ~ H A L Q�~F4 F K y I(L w ~EL({ ~E{PF5K(F�A(B<C+{fB�~�2L2 ~EQWMlC+L �h% <�F?H 2 RJQ@:mCqK(F?H.H<C+L QA(B<R?H<FJL Q<R?F?H.~EI k;: ~EA(MOQWB<F 65%

�!� � � -0= 6 > � � !�-�@ �� =56 #54 � � -$! !�- �� 4�6

c ~ELmH.k?FJQWQ<F|H<F?kJQWMlC+L H�C+L Q;A(B<R?H<FJL Q<R?H.K(FJI54 ~EwO{PC+BWMOQ@:�2 F?H.B<FJw ~EQWMONPF32 FJL QxHWM'2 A(wlF?H�A C+I(B;QWB�~ELmH[DGC+B@2 FJBK(F?H {fB�~�2L2 ~EMOB<F?H H�~ELmH k : ~EL({PFJB wlF w ~EL({ ~E{PF B<F?k?C+L(L I % <�F?H QWB�~ELmH[DGC+B@2 ~EQWMlC+LmH A FJI(NPFJL Q B<FJLmK B<F K(F?H{fB�~�2L2 ~EMOB<F?H3~EL ~Ew'AqH�~�((wlF?H;A ~EB0K(F?H 2 RJQ@:mCqK(F?H0F>G kc~+k?F?H %

�� .�� !��

j C+B<H _ I y I(L ~EL ~Ew'A H<FJI(B�k?C+LmHWQWBWI(MOQ�I(LmF;K(RJBWMONf~EQWMlC+LM� MOw K(C+MOQ�k :mC+MlHWMOB d k : ~/_ ImF0RJQ�~EA F�wlF0LmC+L5�zQ<FJB@2 MOL ~Ewd B<F32 A(w ~+k?FJB FJQ w ~ B 0J{fwlF K(F A(B<CqK ImkJQWMlC+L d I(QWMOwOMlH<FJB A C+I(B wlF B<F32 A(w ~+k?FJB % j F k :mC+My4 K(F w ~ B 0J{fwlF K(FA(B<CqK ImkJQWMlC+L A C+I(Nf~EL Qxkc~EImH<FJBxK(F?H0A(B<C/((w1032 F?H � Q<C+I(Q<F5H�R _ ImFJLmk?F5K(F k;:mC+My4 LmF A(B<C K I(MlH^~EL Q3A ~+HvLmR?k?F?H �H�~EMOB<F32 FJL Q�I(LmF;K(RJBWMONf~EQWMlC+L K(F w ~3k : ~FElLmF��m2��32 F�H<M(I(LmF�K(RJBWMON+~EQWMlC+L Fh4 MlHWQ<F ( FJwmFJQT((MlFJL � �fMOw(N+~EI(Q�2 MlFJI54~?NPC+MOB I(LmF.{fB�~�2L2 ~EMOB<FxC$; MOw Fh4 MlHWQ<F0I(L�2 MOL(M'2�I�2 K y ~�2=((MO{fI(MOQ<RxKm~ELmH�wlF.k;:mC+My4 K(F?H�B 0J{fwlF?H K(F0A(B<CqK Imkh�QWMlC+L wlC+B<H _ I y C+L k?C+L(L ~EMOQ0wlF?H;A(B<C k;: ~EMOLmH0H@AB2,( C+wlF?H�Q<FJB@2 MOL ~EI54 d K(RJBWMONPFJB d A ~EBWQWMOB0K I LmC+L5�zQ<FJB@2 MOL ~Ew dB<F32 A(w ~+k?FJB %t L5kc~+HH_ I(M A FJI(Q H<F�A(B<CqK I(MOB<F�F?H<Q)k?FJwOI(M K(F 2 I(wOQWMOA(wlF?H B 0J{fwlF?H�K(F�A(B<CqK ImkJQWMlC+L5A ~EBWQ�~E{PFc~EL Q�I(L�A(B<Rh\�4(F

k?C/2L2�I(L % <�C+LmHWMlK(RJB<C+LmHoA ~EB Fh4 F32 A(wlF I(LmF :!A A C+Q@:mRJQWM1_ ImF {fB�~�2L2 ~EMOB<F K(F?H RJLmC+Lmk?R?H K y ~EwOQ<FJBWL ~EQWMONPF?HKm~ELmH�I(L w ~EL({ ~E{PF�K(FxA(B<C+{fB�~�2L2 ~EQWMlC+L ,

S → {�z E ��5u&| S | {�z E ��5u&| S u�B~&u S | . . .

E → . . .

� L k?C+LmHWQ�~EQ<F�MlkJM�_ ImF3wlF?H0K(FJI54 B 0J{fwlF?H0K(FxA(B<CqK ImkJQWMlC+L A C+I(B;wzy ~EwOQ<FJBWL ~EQWMONPF�A ~EBWQ�~E{PFJL QvA(wOImHWMlFJI(B<H0H@AB2 �( C+wlF?HxFJL#A(B<Rh\�4 F�� FJQxFJL#A(wOImH+_ I y FJwOwlF?H|k?C/2L2 FJLmk?FJL Q|Q<C+I(Q<F?H|wlF?HxK(FJI54 A ~EB3wlF 2��32 FoQ<FJB@2 MOL ~Ew � {�z �h%. C+I(B RJNqMOQ<FJB k?FJQWQ<F H<MOQWI ~EQWMlC+LM��MOw0HWIHG Q K(F Dz~+kJQ<C+BWMlH<FJB wlF A(B<Rh\�4(F k?C/2L2 I(L FJL kJB<Rc~EL Q I(L LmC+I(NPFc~EILmC+L5�zQ<FJB@2 MOL ~Ew B<FJQ�~EB<Km~EL Q�wlFvk;:mC+My4 FJL QWB<F3wlF?H�K(FJI54 Q<FJB@2 MOL ~EMlH<C+LmH0~EI�2 C/2 FJL Q0C$; wlFvA(B<Rh\�4 F3k?C/2L2 I(L~EI(B�~ RJQ<RxB<F?k?C+L(L I %j y ~EwO{PC+BWMOQ@:�2 F|K(FvDz~+kJQ<C+BWMlH�~EQWMlC+L d { ~EImk :mF|F?HWQ K(C+L(LmR d w ~=\m{fI(B<F ]�%'$&% p w k?C+LmHWMlHWQ<F d QWB�~EMOQ<FJB�Q<C+I(B d

Q<C+I(B%Q<C+ImH�wlF?H�LmC+L5�zQ<FJB@2 MOL ~EI54 �qFJQ%A C+I(B�k;: ~+kJI(L K(F.k?F?H�K(FJBWL(MlFJB<H�� d MlK(FJL QWMy\ FJB�wlF?H%A(B<Rh\�4 F?H�k?C/2L2�I(LmH��d wlF?H;Fh4 QWB�~EMOB<F�K(F?H0A(B<C K ImkJQWMlC+LmH.k?C+Lmk?FJBWLmR?F?H�� d MOL QWB<CqK I(MOB<F�I(L LmC+I(NPFc~EI LmC+L5�zQ<FJB@2 MOL ~Ew)Km~ELmH.k : ~/_ ImFkc~+H d w ~*\mL K I A(B<Rh\�4(F3k?C/2L2�I(L ~EMOLmHWM Fh4 QWB�~EMOQ FJQ d K(Rh\mL(MOB�A C+I(B�wlF.LmC+I(NPFc~EI LmC+L5�zQ<FJBWB@2 MOL ~Ew ~EI(Q�~EL QK(FxB 0J{fwlF?H;K(F|A(B<C K ImkJQWMlC+L ~cNPF?k�k;: ~/_ ImF|H<IHGL4 FxK MlHWQWMOLmkJQ %

� qO�!�Rk� "� � �y� . C+I(B.w ~o{fB�~�2L2 ~EMOB<F5K(F?H0~EwOQ<FJBWL ~EQWMONPF?HvA(B<R?k?R?K(FJL Q<F�� C+L A FJI(Q0MlK(FJL QWMy\ FJB.k?C/2L2 F�A(B<Rh�\�4(Fxk?C/2L2�I(L w ~5A C+BWQWMlC+L α = {�z E ��5u&| S

% <�F?kJM LmC+ImH�w ~EMlH<H�F3wlF?H0HWIHGL4(F?H β1 = ε FJQ β2 = u��5~&u S%

j F?HvA(B<CqK ImkJQWMlC+LmH.LmC+L5� k?C+Lmk?FJBWLmR?F?H|A ~EB.w ~ DG~+kJQ<C+BWMlH^~EQWMlC+L LmF5H<C+L QvA ~+H3k?C+L(L ImF?H3MlkJM ��2 ~EMlH.K MlH�C+LmH _ ImFγ = . . .

% � L C/((QWMlFJL Qv~EwlC+B<H0w ~5{fB�~�2L2 ~EMOB<F|QWB�~ELmH[DGC+B@2 R?F�,S → {�z E ��5u/| S S′ | . . .

S′ → ε | u��B~mu S

E → . . .2

]�%87 a B�~ELmH[D C+B@2 ~EQWMlC+LmHvK(F3{fB�~�2L2 ~EMOB<F?H ]�-

nqC+MOQ.I(LmF {fB�~�2L2 ~EMOB<F G �mwzy ~EwO{PC+BWMOQ@:�2 FoA(B<CqK I(MOQ0I(LmF {fB�~�2L2 ~EMOB<F G′ R _ I(MON+~EwlFJL Q<F5C$; Q<C+ImH0wlF?HA(B<Rh\�4 F?H k?C/2L2 I(LmH wlF?H A(wOImH wlC+L({PH FJL QWB<F wlF?H A ~EBWQWMlF?H K B<C+MOQ<F?H K(F A(B<CqK ImkJQWMlC+LmH ~EI(B<C+L Q RJQ<RDG~+kJQ<C+BWMlH<R?H %$&% MP��QM �OGU� MOw�Fh4qMlHWQ<FxK(F?H;A(B<C K ImkJQWMlC+LmHv~?NPF?k|A(B<Rh\�4(Fxk?C/2L2�I(L ��I"��

�5% � ��GU� k : ~/_ ImFxLmC+L5�zQ<FJB@2 MOL ~Ew A� ��IK��

75% QWB<C+I(NPFJB;wlFxA(wOImH�wlC+L({ A(B<Rh\�4(F α k?C/2L2�I(L d K(FJI54~EwOQ<FJBWL ~EQWMONPF?H.K(F3A(B<CqK ImkJQWMlC+LmH0C+I A(wOImH %]�% �`I

α 6= ε�� K��F�

-5% B<F32 A(w ~+k?FJB.Q<C+I(Q<F?H;wlF?H A �zA(B<C K ImkJQWMlC+LmH A→ αβ1|αβ2|...|αβn|γ� C$; γB<FJA(B<R?H<FJL Q<F|Q<C+I(Q<F?H0wlF?H0~EwOQ<FJBWL ~EQWMONPF?H _ I(M LmFxk?C/2L2 FJLmk?FJL QvA ~+H�A ~EB α �A ~EB;wlF?H;A(B<C K ImkJQWMlC+LmH�,

A→ αA′|γA′ → β1|β2|...|βnST�

ST�

�� ]�%'$ � [ wO{PC+BWMOQ@:�2 F|K(FxDG~+kJQ<C+BWMlH�~EQWMlC+L d { ~EImk :mF

�� # �� !�

. ~EB.{fB�~�2L2 ~EMOB<F|B<R?kJI(B<HWMONPF d { ~EImk;:mF�� C+L FJL Q<FJLmKD, �F��R��I"�� FE!l�G��`I �� GUl� ��.- I(LmFv{fB�~�2L2 ~EMOB<F|F?HWQ�K MOQ<FvB<R?kJI(B<HWMONPF d { ~EImk :mF|H<MFJwOwlF ~+K52 FJQ|~EI 2 C+MOLmH3I(LmFoH<R _ ImFJLmk?F K(FoK(RJBWMON+~EQWMlC+LmHxK(Fow ~ DGC+B@2 F A

∗⇒ Aα C$; A F?HWQ

I(L LmC+L5�zQ<FJB@2 MOL ~Ew %X LoDG~EMOQ��EwlF�k?C+Lmk?FJA(Q�K(F B<R?kJI(B<HWMONqMOQ<R d { ~EImk :mF;F?H<Q)Q<C+I(Q d Dz~EMOQ�HWM'2 MOw ~EMOB<F d w ~vB<R?kJI(B<HWMON MOQ<R Q<FJwOwlF _ I y C+L

wzy ~EA(A(B<FJLmK Km~ELmHvwlF?H.w ~EL({ ~E{PF?HxK(F A(B<C+{fB�~�2L2 ~EQWMlC+L , I(L LmC+L5�zQ<FJB@2 MOL ~Ew�H<F5K(RJBWMONPF I(L $ C+I A(wOImH<MlFJI(B<HRJQ�~EA F?HxFJL I(LmFoH<R _ ImFJLmk?FoK(FoH@A!2=( C+wlF?HvQ<FJB@2 MOL ~EI54#FJQ3LmC+L5�zQ<FJB@2 MOL ~EI54#C$; MOw�~EA(A ~EB�~FElQ|FJL A(B<F32 M10JB<FA CfHWMOQWMlC+L % n M I(LmFxQ<FJwOwlFxK(RJBWMONf~EQWMlC+L Fh4qMlH<Q<F�� MOw F?HWQ�A CfH�HWM'((wlFxK(F3B<RJA RJQ<FJB�w ~ H<R _ ImFJLmk?FxK y ~EA(A(wOMlkc~EQWMlC+LmHvK(FB 0J{fwlF?H;K(F3A(B<CqK ImkJQWMlC+L d LmC+I(NPFc~EI HWI(B�wlF A FJL A(B<F32 M10JB<F�A CfH<MOQWMlC+L K(F3w ~5A(B<C+Q<C+A�:(B�~+H�FxB<R?HWI(wOQ�~EL Q<F�� FJQ~EMOLmHWM K(F|H<I(MOQ<F�2 �=T @ �J@�TA8 �# %

<�FJBWQ�~EMOLmF?H|K(F?H|~EA(A(B<C k;:mF?H|K y ~EL ~Ew'A H<FL_ ImF5LmC+ImH3NPFJBWB<C+LmH�~EI�k;: ~EA(MOQWB<F 6 LmFoHcy ~EA(A(wOM1_ ImFJL Q|A ~+H|~EIkc~+HvK(F?H0{fB�~�2L2 ~EMOB<F?HvB<R?kJI(B<HWMONPF?H d { ~EImk;:mF % j ~ A CfH<HWM'((MOwOMOQ<R�K(F�QWB�~ELmH[DGC+B@2 FJBvH@A HWQ<R32 ~EQWM1_ ImF32 FJL QvI(LmF{fB�~�2L2 ~EMOB<F G B<R?kJI(B<HWMONPF d { ~EImk;:mF�FJL I(LmFx{fB�~�2L2 ~EMOB<F G′ R _ I(MON+~EwlFJL Q<F,_ I(M LmFxH<C+MOQ;A ~+H�B<R?kJI(B<H<MONPF d{ ~EImk :mF F?HWQ;K(C+LmkxMOL Q<RJB<F?H<H�~EL QvKm~ELmH;k?F?H0kc~+H0K(F \m{fI(B<F %r0F32 ~EB _ ImC+LmH _ I y MOw LmF3Hcy ~E{fMOQ A ~+H�I(L(M1_ ImF32 FJL Q0K(FvB<R?kJI(B<HWMON MOQ<R d { ~EImk :mF3M'2L2 R?K M ~EQ<F�� kfy F?HWQ � d � K MOB<F

C$; wlF H@AB2,( C+wlF LmC+L5�zQ<FJB@2 MOL ~Ew�~EA(A ~EB�~FElQ ~EI K(R3((I(Q K(F wzy I(LmF K(F?H A ~EBWQWMlF?H K B<C+MOQ<F?H K(F H<F?H A(B<C+A(B<F?HA(B<CqK ImkJQWMlC+LmH % f C+LM��MOw;Hcy ~E{fMOQ A(wOImH {PRJLmRJB�~EwlF32 FJL Q K y RJwOM'2 MOLmFJB Q<C+I(Q<F B<R?kJI(B<HWMONqMOQ<R d { ~EImk :mF Km~ELmH w ~{fB�~�2L2 ~EMOB<F��_ I y FJwOwlF|H<C+MOQ;K MOB<F?kJQ<F�C+I MOLmK MOB<F?kJQ<F %

� qO�!�Rk� "� � �1# j ~o{fB�~�2L2 ~EMOB<F HWI(MON+~EL Q<F|F?HWQ�B<R?kJI(B<HWMONPF d { ~EImk :mF&,E → E � E

A(I(MlH _ I y FJwOwlFxk?C+L QWMlFJL Q0I(LmF3B<R?kJI(B<HWMONqMOQ<R d { ~EImk :mFxM'2L2 R?K M ~EQ<F�HWI(B�wlF3LmC+L5�zQ<FJB@2 MOL ~Ew E% j ~5{fB�~�2L2 ~EMOB<F

HWI(MONf~EL Q<F3F?HWQ�RJ{ ~EwlF32 FJL Q�B<R?kJI(B<HWMONPF d { ~EImk :mF�2 ~EMlH�LmF0A CfH<H 0?K(F0A ~+H K(F0B<R?kJI(B<HWMONqMOQ<R?H d { ~EImk :mFvM'2L2 Rh�

]�6 j ~EL({ ~E{PF?H;LmC+L5� k?C+L Q<Fh4 QWImFJwlH�� {fB�~�2L2 ~EMOB<F?H0FJQ.~EI(Q<C/2 ~EQ<F?H d A(MOwlF

K M ~EQ<F?H!,S → Aα

A → Sβ | . . .

A(I(MlH _ I y C+L A FJI(Q;K(RJBWMONPFJB S+⇒ Sβα

%2

<�C+LmHWMlK(RJB<C+LmH3K y ~�( C+B<K I(LmF*2 RJQ@:mCqK(F K y RJwOM'2 MOL ~EQWMlC+L#K(F?H.B<R?kJI(B<HWMONqMOQ<R?H d { ~EImk :mF5M'2L2 R?K M ~EQ<F?H % j ~B<R?kJI(B<HWMONqMOQ<R d { ~EImk :mF�M'2L2 R?K M ~EQ<F�H<F3A(B<R?H�FJL Q<F�Km~ELmH;I(LmFx{fB�~�2L2 ~EMOB<F�H<C+ImH;w ~ D C+B@2 F|H<I(MON+~EL Q<F�,

A → Aα | β

C$; β F?HWQ I(LmF�H�R _ ImFJLmk?F K(F H@AB2,( C+wlF?H LmF�K(R3((I(Q�~EL Q�A ~+H A ~EB A%/. C+I(B�k?C/2 A(B<FJLmK B<F;k?C/2L2 FJL Q�RJwOM'2 MOLmFJB

w ~�B<R?H<I(B<HWMON MOQ<R d { ~EImk;:mF%M'2L2 R?K M ~EQ<F��EMOwPDz~EI(Q�Fh4m~�2 MOLmFJB wlF?H)K(RJBWMONf~EQWMlC+LmH�A CfH<HWM'((wlF?H d wzy ~EMlK(F�K(F%H<F?H�B 0J{fwlF?HK(FxA(B<CqK ImkJQWMlC+L %�. ~EBWQ�~EL Q3K(F A �mC+L A FJI(Q0C/((Q<FJL(MOB!,

A ⇒ βA ⇒ Aα ⇒ βαA ⇒ Aα ⇒ Aαα ⇒ βααA ⇒ Aα ⇒ Aαα ⇒ Aααα ⇒ . . .� L H<F B<FJLmK K(C+Lmk k?C/2 A(Q<F _ ImF wlF?HoH<R _ ImFJLmk?F?H _ I(M�A FJI(NPFJL Q �JQWB<F K(RJBWMONPR?F?H d A ~EBWQWMOB5K(F A H<C+L Q

DGC+B@2 R?F?H;K y I(LmF�~EA(A ~EBWMOQWMlC+L K(F β HWI(MONqMlFxK(F Z � $ C+I A(wOImHWMlFJI(B<H�B<RJA RJQWMOQWMlC+LmH;K(F α% <�C+LmHWQWBWI(MlH<C+LmH0K(C+Lmk

I(LmFx{fB�~�2L2 ~EMOB<F�A(B<C K I(MlH�~EL Q;wlF+2��32 Fxw ~EL({ ~E{PF FJQ)_ I(M LmFxH<C+MOQ;A ~+H�B<R?kJI(B<HWMONPF d { ~EImk :mF+2 ~EMlH0A(wOI(Q��+QB<R?kJI(B<HWMONPF d K B<C+MOQ<F�,

A → βA′

A′ → αA′ | ε

j ~ wOMO{fLmF � - � Km~ELmH wzy ~EwO{PC+BWMOQ@:�2 F�K(F.w ~,\m{fI(B<F ]�% � {PRJLmRJB�~EwOMlH<Fxk?FJQWQ<FvMlK(R?F3A C+I(B�Q<C+I(Q<FvB<R?kJI(B<HWMONqMOQ<R d{ ~EImk :mF�M'2L2 R?K M ~EQ<F�� kfy F?HWQ � d � K MOB<F|wlC+B<H _ ImF|wlF?H�A(B<C K ImkJQWMlC+LmH.H<C+L Q.K(Fxw ~ D C+B@2 F&,

Ai → Aiα1 | . . . | Aiαm | β1 | . . . | βn

_ ImF3wzy C+L B<F32 A(w ~+k?F|A ~EB:,Ai → β1A

′i | . . . | βnA′

i

A′i → α1A

′i | . . . | αmA′

i | ε

� qO�!�Rk� "� � � <�C+LmHWMlK(RJB<C+LmH;w ~ {fB�~�2L2 ~EMOB<F|K(F?H0Fh4 A(B<F?H<HWMlC+LmH0~EBWMOQ@:�2 RJQWM1_ ImF?H0H<I(MON+~EL Q<F�,E → E � T | T

T → T � F | F

F → ( E - | {F}. C+I(B RJwOM'2 MOLmFJB5w ~ B<R?kJI(B<HWMONqMOQ<R d { ~EImk :mF M'2L2 R?K M ~EQ<F HWI(B E � C+L A(B<FJLmK β = T FJQ α = � T A C+I(BC/((Q<FJL(MOB!,

E → TE′

E′ → � TE′ | ε

c F 2��32 F��(A C+I(B�RJwOM'2 MOLmFJB;w ~ B<R?kJI(B<HWMONqMOQ<R d { ~EImk :mF3M'2L2 R?K M ~EQ<F�HWI(B�wlF3H@A!2=( C+wlF T � C+L A(B<FJLmK β = F

]�%87 a B�~ELmH[D C+B@2 ~EQWMlC+LmHvK(F3{fB�~�2L2 ~EMOB<F?H ]!C

nqC+MOQ�I(LmF%{fB�~�2L2 ~EMOB<F G H�~ELmH)k3AqkJwlF � K(RJBWMON+~EQWMlC+LoK(F%w ~�D C+B@2 F A∗⇒ A

� FJQ�H�~ELmH�A(B<CqK ImkJQWMlC+L N MlK(F� M % F % K(F0w ~3DGC+B@2 F A→ ε

� � wzy ~EwO{PC+BWMOQ@:�2 F.A(B<CqK I(MOQ%I(LmF.{fB�~�2L2 ~EMOB<F G′ R _ I(MONf~EwlFJL Q<F3H�~ELmH�B<R?kJI(B �HWMON MOQ<R d { ~EImk :mF %$&% � L C+B<K(C+L(LmF�wlF?H�LmC+L5�zQ<FJB@2 MOL ~EI54 A1

� A2� %'%'% � An

%�5% k �QG��

i ,87 $ �[ImH _ I y d n� ��I"�F�

75% k �QG��j ,87 $ �[ImH _ I y d i− 1

��I"��]�% B<F32 A(w ~+k?FJB0Q<C+I(Q<F?H�wlF?H0A(B<C K ImkJQWMlC+LmH Ai → Ajγ

A ~EB�wlF?H;A(B<C K ImkJQWMlC+LmHAi → δ1γ|δ2γ|...|δkγ �mC$; Aj → δ1|δ2|...|δk

H<C+L Q;Q<C+I(Q<F?H;wlF?HAj�zA(B<C K ImkJQWMlC+LmH.k?C+I(B�~EL Q<F?H %ST�

-5% RJwOM'2 MOLmFJB;wlF?H�B<R?kJI(B<H<MON MOQ<R?H d { ~EImk :mF|M'2L2 R?K M ~EQ<F?HvK(F?H Ai�zA(B<CqK ImkJQWMlC+LmH d wzy ~EMlK(F|K(F

w ~5QWB�~ELmH[DGC+B@2 ~EQWMlC+L HWI(MONf~EL Q<F&,Ai → Aiα1|...|Aiαm|β1|...|βnK(FJN MlFJL Q!,Ai → β1A

′i|...|βnA′

i

A′i → α1A

′i|...|αmA′

i|εST�

�� ]�% � � X wOM'2 MOL ~EQWMlC+L K(F?H0B<R?kJI(B<HWMON MOQ<R?H d { ~EImk :mF

FJQ α = � F A C+I(B;C/((Q<FJL(MOB!,T → FT ′

T ′ → � FT ′ | ε

2

j y ~EA(A(wOMlkc~EQWMlC+L K(F wzy ~EwO{PC+BWMOQ@:�2 F.K(F w ~ \m{fI(B<F ]�% � NqMlH<F d RJwOM'2 MOLmFJB�wlF?H�B<R?kJI(B<H<MON MOQ<R?H d { ~EImk :mF0~EI(Q�~EL QK MOB<F?kJQ<F?H)_ I y MOLmK MOB<F?kJQ<F?H % j F3A(BWMOLmkJMOA FxK(F3wzy ~EwO{PC+BWMOQ@:�2 F|k?C+LmHWMlHWQ<F d C+B<K(C+L(LmFJB�wlF?H LmC+L5�zQ<FJB@2 MOL ~EI54 K(F Zd

n A(I(MlH d wlF?H QWB�~EMOQ<FJB�Km~ELmH wzy C+B<K B<F�kJB<C+MlH<H^~EL Q�K(F 2 ~EL(M10JB<F d k?Fb_ I y d wzy RJQ�~EA F i �EQ<C+I(Q<F?H�wlF?H)B<R?kJI(B<HWMON MOQ<R?Hd { ~EImk;:mF M'2L2 R?K M ~EQ<F?H5K(FN2��32 F�_ ImF Q<C+I(Q<F?H�wlF?H�B<R?kJI(B<HWMONqMOQ<R?H d { ~EImk :mF MOLmK MOB<F?kJQ<F?H=_ I(M � K(R3((I(Q�~EL QA ~EB|I(L�LmC+L5�zQ<FJB@2 MOL ~Ew K y MOLmK Mlk?F j ≤ i � A ~+H<H<FJL Q�A ~EB|I(L�LmC+L5�zQ<FJB@2 MOL ~Ew k ≤ i

% <�FJQ|MOL Nf~EBWM ~EL QoRJQ�~EL Q2 ~EMOL Q<FJL I d k : ~/_ ImF MOQ<RJB�~EQWMlC+LM�+wlC+B<H _ ImF i K(FJN MlFJL Q�RJ{ ~Ew d n �!Q<C+I(Q<F?H wlF?H)B<R?kJI(B<HWMON MOQ<R?H d { ~EImk :mF�K MOB<F?kJQ<F?HC+I MOLmK MOB<F?kJQ<F?Hv~EI(B<C+L Q.RJQ<RxRJwOM'2 MOLmR?F?H %

. C+I(B ~EBWBWMONPFJB d k?FJQ C/(5�WF?kJQWM D � wzy MlK(R?F d k;: ~/_ ImF#RJQ�~EA F#F?HWQ K y I(QWMOwOMlH<FJB wlF Dz~EMOQ _ ImF HWMxC+L ~ I(LmF{fB�~�2L2 ~EMOB<F C$; A → Bα FJQ B → β � ~EwlC+B<How ~ {fB�~�2L2 ~EMOB<F C/((Q<FJL ImF FJL B<F32 A(w ~$�c~EL Q wlF } ~EIK(R3((I(Q3K(F|w ~ A ~EBWQWMlF5K B<C+MOQ<F5K(F�w ~ A(B<C K ImkJQWMlC+L HWI(B A A ~EBvw ~ A ~EBWQWMlF5K B<C+MOQ<F K(F�w ~ A(B<CqK ImkJQWMlC+L H<I(B B �kfy F?HWQ � d � K MOB<F�~cNPF?kxw ~5A(B<CqK ImkJQWMlC+L A → βα F?HWQ;R _ I(MONf~EwlFJL Q<F d w ~5{fB�~�2L2 ~EMOB<FxMOL(MOQWM ~EwlF %�. ~EB0k?F3{PFJL(B<FK(F B<F32 A(w ~+k?F32 FJL Q��)C+L�DG~EMOQ�FJL H<C+BWQ<FN_ ImF Q<C+I(Q<F B<R?kJI(B<H<MON MOQ<R MOLmK MOB<F?kJQ<F d wzy RJQ�~EA F i A ~+H<H^~EL Q�A ~EB I(LLmC+L5�zQ<FJB@2 MOL ~Ew�K y MOLmK Mlk?F j ≤ i K(FJN MlFJL Q FJL�Dz~EMOQ�I(LmF B<R?kJI(B<HWMONqMOQ<R K MOB<F?kJQ<F % <�FJQWQ<F B<R?kJI(B<HWMONqMOQ<R K MOB<F?kJQ<FF?HWQ�~EwlC+B<H RJwOM'2 MOLmR?F HWM'2 A(wlF32 FJL Q�A ~EB|w ~ QWB�~ELmHWD C+B@2 ~EQWMlC+L {PRJLmRJB�~EwlF A(B<R?k?R?K(FJL Q<F % j y ~EwO{PC+BWMOQ@:�2 F K(F w ~\m{fI(B<F ]�% � DGC+B@2 ~EwOMlH<F|k?FJQWQ<F|MlK(R?F %� qO�!�Rk� "� � �Ks <�C+LmHWMlK(RJB<C+LmH;w ~ {fB�~�2L2 ~EMOB<F|HWI(MONf~EL Q<F&,

S → A � | +A → A � | S }

] � j ~EL({ ~E{PF?H;LmC+L5� k?C+L Q<Fh4 QWImFJwlH�� {fB�~�2L2 ~EMOB<F?H0FJQ.~EI(Q<C/2 ~EQ<F?H d A(MOwlF

� B<K(C+L(LmC+LmH.wlF?H�LmC+L5�zQ<FJB@2 MOL ~EI54 FJL k?C+LmHWMlK(RJB�~EL Q _ ImF S ~5wzy MOLmK Mlk?F $ FJQ A ~5wzy MOLmK Mlk?F �5%� 8SR �(2�8UT '$@�� i = 1

<�C/2L2 F%MOwPL y A|~;A ~+H K(F�LmC+L5�zQ<FJB@2 MOL ~EI54 A(B<R?k?R?K(FJL Q<H��!MOw HWIHG Q)K y RJwOM'2 MOLmFJB�wlF?H B<R?kJI(B<HWMON MOQ<R?H d { ~EImk;:mFM'2L2 R?K M ~EQ<FoHWI(B;wlF H@A!2=( C+wlF S

% <�C/2L2 F5MOw L y A ~ A ~+H.K(F�Q<FJwOwlF�B<R?kJI(B<HWMONqMOQ<R d { ~EImk :mF5M'2L2 R?K M ~EQ<F�� C+LLmF|k;: ~EL({PFxA ~+H;w ~5{fB�~�2L2 ~EMOB<F %� 8SR �(2�8UT '$@�� i = 2j ~ A(B<CqK ImkJQWMlC+L A → S } Dz~EMOQv~EA(A ~EB�~FElQWB<F5I(L LmC+L5�zQ<FJB@2 MOL ~Ew K(R � d QWB�~EMOQ<R d { ~EImk;:mFoK(F|w ~ A ~EBWQWMlFK B<C+MOQ<F;K(F�w ~vB 0J{fwlF % � L wlF B<F32 A(w ~+k?F0K(C+Lmk�A ~EB%Q<C+I(Q<F?H�wlF?H�A ~EBWQWMlF?H%K B<C+MOQ<F?H�K(F?H�A(B<CqK ImkJQWMlC+LmH%k?C+I(B�~EL Q<F?HHWI(B;k?F|H A!2=( C+wlF��(k?F*_ I(M LmC+ImH;K(C+L(LmF�wlF?H�A(B<C K ImkJQWMlC+LmH.HWI(MONf~EL Q<F?H;A C+I(B A ,

A → A � | A �&} | +!}X LmHWI(MOQ<F��(RJwOM'2 MOLmC+LmH wlF?H B<R?kJI(B<H<MON MOQ<R?H M'2L2 R?K M ~EQ<F?H;H<I(B A

%!. C+I(B0k?FJw ~H� C+L ~ α1 = �� α2 = �m} FJQ β1 =+!} % � L C/((QWMlFJL Q|K(C+Lmk wlF?H0B 0J{fwlF?H3K(F A(B<C K ImkJQWMlC+L#HWI(MONf~EL Q<F?H�_ I(M B<F32 A(w ~+k?F5wlF?HvB 0J{fwlF?H3K(F�A(B<CqK ImkJQWMlC+LHWI(B A A(B<R?k?R?K(FJL Q<F?HvKm~ELmH�w ~o{fB�~�2L2 ~EMOB<F�B<R?HWI(wOQ�~EL Q<F�,

A → +!} A′

A′ → � A′ | �&} A′ | ε

2

� ��

� ��

c ~ELmH k?F k;: ~EA(MOQWB<F��LmC+ImH ~EwOwlC+LmH MOL QWB<C K I(MOB<F wlF?H k?C+Lmk?FJA(Q<H K I'w ~EL({ ~E{PF � ^ j � K(C+L Q wlF�( ~EwOMlH�~E{PFHWQWBWImkJQWI(B<FJw ~EMOLmHWM�_ ImF;wlF?H�K(F?H<kJBWMOA(QWMlC+LmH�K(F�K(C kJI�2 FJL Q<H%A ~EB c a c FJQ�A ~EB%H�k :mR32 ~+H % f C+ImH%~EwOwlC+LmH�RJ{ ~EwlFh�2 FJL Q)Dz~EMOB<F�I(L5A ~EB�~EwOw10JwlF FJL QWB<F�wlF?H�2 CqK(F?H K(F%K(F?H<kJBWMOA(QWMlC+LmH�K(F�K(CqkJI�2 FJL Q<H � ^ j FJQ wlF?H){fB�~�2L2 ~EMOB<F?H�FJQFJL QWB<F0wlF?H�K(CqkJI�2 FJL Q<H � ^ j FJQ�wlF?H�~EB@((B<F?H%K y ~EL ~Ew'A H<F;A C+I(B�K(F?H�A�:(B�~+H<F?H�K(F�w ~EL({ ~E{PF;LmC+L5� k?C+L Q<Fh4qQWImFJwlH %

� �� -;=��0- �;4 � �5-;: � 6 4�686 � !�-;=.@ � 13254�6

� ^ j F?HWQ I(L w ~EL({ ~E{PF HWQ�~ELmKm~EB<K K(F K(F?H<kJBWMOA(QWMlC+L FJQ K y R?k : ~EL({PF?H K(F K(CqkJI�2 FJL Q<H HWQWBWImkJQWI(B<R?H % pswF?HWQ;MlH�HWI K y I(LmF wlC+L({fImF|QWB�~+K MOQWMlC+L D C+LmK(R?F d w ~5DGC+MlH0Km~ELmH.wlF?H0HWQ�~ELmKm~EB<K(HvK(F�K(F?H�kJBWMOA(QWMlC+LmH.K(F K(C+L(LmR?F?Hk?C/2 A(wlFh4(F?H ~PA ~EL Q�K(C+L(LmR.L ~EMlH<H�~ELmk?F3~EI w ~EL({ ~E{PF|n ��^ j FJQ Km~ELmH%wlF?H�HWQ�~ELmKm~EB<K(H K(FvK(F?H<kJBWMOA(QWMlC+L K(F.w ~A(B<R?H<FJL Q�~EQWMlC+L K(F?H;K(CqkJI�2 FJL Q<HvK(C+L Q0F?H<Q;MlH<HWI 9 a ^ j % � ^ j F?HWQ;HWQ�~ELmKm~EB<K MlH�RxA ~EB;wlF�� 7 < %� ^ j F?HWQ DGC+LmK(RxHWI(B I(L k?C+Lmk?FJA(Q�QWB 0?H;HWM'2 A(wlF ,qwlF&%(2$) T 2�6*: >8 �� < 8 ��P*>) % j y MlK(R?FxK I ( ~EwOMlH^~E{PFxHWQWBWImkh�

QWI(B<FJw F?HWQ�K(FvB<FJLmK B<FvFh4 A(wOMlkJMOQ<F3w ~5HWQWBWImkJQWI(B<F3K y I(L K(C kJI�2 FJL Q;FJL K(R?k?C+I(A ~EL Q;k?F3K(C kJI�2 FJL Q;FJL A ~EBWQWMlF?H2 ~EB _ ImR?F?H|A ~EB K(F?H,( ~EwOMlH<F?H,_ I(M�MOLmK M1_ ImFJL Q wlF K(R3((I(Q�FJQ w ~�\mL�K(F k;: ~+kJI(LmF K(F k?F?H�A ~EBWQWMlF?H FJQ H<C+ImH �A ~EBWQWMlF?H % c ~ELmH5w ~ Q<FJB@2 MOLmC+wlC+{fMlF � ^ j �)I(LmF A ~EBWQWMlF K(F K(C kJI�2 FJL QL( ~EwOMlH<R?F Hcy ~EA(A FJwOwlF.R9)WR>#&*>@Q8 % t LmF( ~EwOMlH<F F?H<Q|LmC+Q<R?F FJL QWB<F H@AB2,( C+wlF?H|A(wOImH�A FJQWMOQ y � y FJQ�A(wOImH|{fB�~ELmK y � y FJQ�A C+BWQ<F I(L�LmC/2 % t LmFp( ~EwOMlH<FC+I(NqB�~EL Q<F5LmF|A C+BWQ<F,_ ImF�wlF�LmC/2�K(F�wzy RJwlR32 FJL Q|~EwlC+B<H�_ I y I(L ( ~EwOMlH<F�D FJB@2 ~EL Q<F�A C+BWQ<F�wlF�LmC/2�K(F�wzy RJwlRh�2 FJL QvA(B<R?k?R?K(R5K y I(LmF C/((wOM1_ ImF y �my %�. ~EBvFh4(F32 A(wlF�� K(F?HvRJwlR32 FJL Q<HxK(RJLmC/2L2 R?H |'�F� FJQ��&}�w5u5~�~&u H<FJB<C+L Q�!A ~EB<FJL Q@:mR?H�R?H � A ~EB;wlF?H)( ~EwOMlH<F?H;HWI(MONf~EL Q<F?H�,

� | �� % % % � �/|'�F� �� &}�w5u5~�~&u � % % % � ��&}�w5u5~�~&u �<�FJQWQ<F3LmC+QWMlC+L K(F ( ~EwOMlH^~E{PF.L y F?H<Q�A ~+H�A(B<C+A(B<F d � ^ j � A(I(MlH;_ I y FJwOwlFxRJQ�~EMOQ�K(R � d A(B<R?H�FJL Q<FxFJL n ��^ j

FJQ.FJL 9 a ^ j ��_ I(M)F?HWQ;w ~EBW{PF32 FJL Q3A(wOImHvk?C+L(L I % c FxDz~EMOQ�� ^ j DG~EMOQ.I(L ImH�~E{PF K I ( ~EwOMlH�~E{PF5K M0/ RJB<FJL QK(F�k?FJwOI(M K y 9 a ^ j % j y C/(5�WF?kJQWM D�K y 9 a ^ j F?HWQ.K y MOLmK M1_ ImFJB d I(L A(B<C+{fB�~�2L2 F5k?C/2L2 FJL Q3A(B<R?H<FJL Q<FJB3I(LK(CqkJI�2 FJL Q d wzy R?kJB�~EL�C+I#wlF5A(B<C K I(MOB<F H<I(BxA ~EA(MlFJB % j F ( ~EwOMlH�~E{PF K y 9 a ^ j H<FJBWQ|K(C+Lmk d MOLmK M1_ ImFJB|K(F?H2 CqK(F?H5FJQoK(F?H5F>/ FJQ<HoK(F A(B<R?H<FJL Q<FJL Q�~EQWMlC+LM��k?C/2L2 F w ~ 2 MlH<F FJL MOQ�~EwOM1_ ImF C+I FJL {fB�~+H��)C+I FJLmk?C+B<F w ~2 MlH<FxFJL A ~EB�~E{fB�~EA�:mF�� FJQ<k %

X L � ^ j �mwlF+( ~EwOMlH�~E{PF|F?HWQ�I(QWMOwOMlH�RxA C+I(B.H<FJ{&2 FJL Q<FJB.I(L K(C kJI�2 FJL Q.FJL MOL DGC+B@2 ~EQWMlC+LmH0H�R32 ~EL QWM1_ ImFh�2 FJL Qxk?C/:mRJB<FJL Q<F?H % <vy F?HWQx~EMOLmHWMT_ I y FJL�� ^ j � C+L A ~EBWwlF K(F1%(2$) T 92�6* R>#�2$@Q8UT � ��* %O� B��+k?F ~EI ( ~EwOMlH�~E{PFH<R32 ~EL QWM1_ ImF�� ^ j M'2 A CfH<F I(LmF MOLmK(RJA FJLmKm~ELmk?F.FJL QWB<F.k?C+L Q<FJL I FJQ�A(B<R?H<FJL Q�~EQWMlC+L % j Fb( ~EwOMlH�~E{PF0H<R32 ~EL5�QWM1_ ImF3A FJB@2 FJQ0K y MlK(FJL QWMy\ FJB0wlF?H�Q A A F?H�K y MOL DGC+B@2 ~EQWMlC+L k?C+L Q<FJL ImF?H.Km~ELmH;I(L \ k :(MlFJB��(Q A A F?H)_ I(M A FJI(NPFJL QFJLmHWI(MOQ<F.H<FJBWN MOB d K(R?kJMlK(FJB�k?C/2L2 FJL Q wlF?H%A(B<R?H�FJL Q<FJB��B_ ImF;k?F.H<C+MOQ�FJL wlF?H%QWB�~ELmHWD C+B@2 ~EL Q�FJL 9 a ^ j A C+I(B

-&Z j Fxw ~EL({ ~E{PF�� ^ j

I(L�~FG k : ~E{PF d wzy R?kJB�~ELM� FJL A CfHWQ<H�kJBWMOA(QvA C+I(B3wzy M'2 A(B<F?H<HWMlC+L#HWI(B3A ~EA(MlFJB�� C+I#FJL H�C+L L I�2 RJBWM1_ ImF A C+I(BB<FJA(B<CqK ImkJQWMlC+L A ~EB0H@AqL Q@:�0?H�FxK(F|H<C+L NqM ~oK(F?H;FJLmk?FJMOL Q<F?H %

� qO�!�Rk� "� # �" X L ( ~EwOMlH�~E{PF H<R32 ~EL QWM1_ ImF�� C+L#A C+I(BWB�~�2 ~EB _ ImFJBxI(LmFoKm~EQ<FoA ~EBxK(F?H�( ~EwOMlH<F?HxK(F5LmC/2}B�*�5u FJL k :mC+MlHWMlH�H�~EL Q;I(L D C+B@2 ~EQ;HWQ�~ELmKm~EB<K k?C/2L2 F�,

� }B�*�5u � � �� "� �m}B�*�5u �nqFJwlC+L#wzy I(QWMOwOMlH�~EQWMlC+L�K(F k?FJQWQ<FoMOL DGC+B@2 ~EQWMlC+LM� Km~ELmHxI(L#L ~?NqMO{ ~EQ<FJI(B|MOL Q<FJBWLmFJQ�C+I�HWI(B3A ~EA(MlFJB�C+I#FJL5�

k?C+B<F|HWI(B Q<RJwlRJA�:mC+LmF�A C+BWQ�~�((wlF�~cNPF?k|H@AqL Q@:�0?H<F3NPCqkc~EwlF��mk?FJQWQ<FxMOL DGC+B@2 ~EQWMlC+L A C+I(BWB�~ �JQWB<FxA(B<R?H<FJL Q<R?FxA ~EB75$ � Z&- � $PW&65$ � C+I FJLmk?C+B<F 75$ 2 ~EM $PW&65$ �mC+L FJLmk?C+B<F|A ~EB;I(LmFxNPC+My4 K MlH�~EL Q0k?FJQWQ<F�Km~EQ<F %2

. ~EB@2 M�wlF?H|A(B<R?H<FJL Q�~EQWMlC+LmH�A CfH<H<M'((wlF?HxK y I(L�K(C kJI�2 FJL Q�� ^ j � kJMOQ<C+LmHxw ~ A(B<R?H<FJL Q�~EQWMlC+L�H<C+ImH3DGC+B@2 FK(F A ~E{PF��F3(M�%H<C+ImH5D C+B@2 F K(F K(CqkJI�2 FJL Q A ~EA(MlFJB��H<C+ImH5DGC+B@2 F K y M'2 ~E{PF��H<C+ImH5DGC+B@2 F K(F H@A L Q@:�0?H<FNPCqkc~EwlF��FJQ<k % j y MlK(R?F K y � ^ j K(F H�RJA ~EB<FJB MlK(FJL QWMy\ kc~EQWMlC+L�K I k?C+L Q<FJL I K(F H�~ A(B<R?H<FJL Q�~EQWMlC+L HWI(A(A CfH<F_ ImF wzy MOL D C+B@2 ~EQWMlC+L H<I(B5w ~ A(B<R?H�FJL Q�~EQWMlC+LM� _ I(M L y F?HWQ A ~+H Km~ELmHowlF�\ k;:(MlFJB wOI(My� 2��32 F��H<FJB�~#~EA(A C+BWQ<R?FK(F 2 ~EL(M10JB<F MOLmK(RJA FJLmKm~EL Q<F K I�K(CqkJI�2 FJL Q�A ~EBxI(LmF QWB�~ELmH[D C+B@2 ~EQWMlC+L K y I(L�K(CqkJI�2 FJL Q�H<C+I(B<k?F�� ^ jFJL I(LmF|D C+B@2 FxA(B<R?H�FJL Q�~�((wlF � K(C kJI�2 FJL Q 9 a ^ j � K(C kJI�2 FJL Q.A CfHWQ<H<kJBWMOA(Q��5\ k;:(MlFJB.K(F|H�C+LM�mFJQ<k % �h% f C+ImHNPFJBWB<C+LmH;wzy ~+H<A F?kJQ�QWB�~ELmH[DGC+B@2 ~EQWMlC+L K(F�K(C kJI�2 FJL Q.~EI k : ~EA(MOQWB<F �5%

� ��l�GH�R�B�QMP� �� t L K(CqkJI�2 FJL Q�� ^ j F?HWQ I(L \ k :(MlFJB K(C+L Q wlF k?C+L Q<FJL I F?HWQL( ~EwOMlH<R H<FJwlC+L'wlF?H B 0J{fwlF?H K I w ~EL({ ~E{PF

� ^ j % j F�( ~EwOMlH�~E{PF A FJI(Q �JQWB<F MOL QWB<C K I(MOQoQWB 0?H5wOM'( RJB�~EwlF32 FJL Q FJL � ^ j ��FJL K(Rh\mL(MlH<H�~EL Q k : ~/_ ImF DGC+MlH_ ImF LmR?k?F?H<H^~EMOB<F K(F?H5LmC/2 HoK y RJwlR32 FJL Q<H ~EA(A(B<C+A(BWMlR?H d wzy MlK(FJL QWMy\ kc~EQWMlC+L K(F wlFJI(Bok?C+L Q<FJL I % j F?HoB 0J{fwlF?HH@AqL Q�~F4 M1_ ImF?H�K y � ^ j M'2 A CfH<FJL Q;K(F?H�k?C+L QWB�~EMOL Q<F?H0HWI(B w ~�D C+B@2 ~EQWMlC+L K(F?H LmC/2 H�K y RJwlR32 FJL Q<H � H<R _ ImFJLmk?FK(F5kc~EB�~+kJQ 0JB<F?H�~EwOA�: ~EL I�2 RJBWM1_ ImF?H�� K(F?H3kc~EB�~+kJQ 0JB<F?H3QWMOB<FJQxFJQvH<C+I(wOMO{fLmRoC+I#K I A C+MOL Q3k?C/2L2 FJL��c~EL QxA ~EBI(L kc~EB�~+kJQ 0JB<F5~EwOA�: ~�( RJQWM1_ ImF�C+I I(L H<C+I(wOMO{fLmR �(wlF|K(FJI54B�zA C+MOL Q<H0A FJI(Q0~EImH<HWM �JQWB<FxI(QWMOwOMlH<R+2 ~EMlH0MOw�~5I(LmFHWMO{fL(My\ kc~EQWMlC+L HWA R?kJMy\�_ ImF � ~EMOLmH<M�_ ImF�w ~xHWQWBWMlkJQ<F0M'2,((BWMlkc~EQWMlC+L K(F?H ( ~EwOMlH<F?H � A ~EB<FJL Q@:mR?H�~E{PFvk?C+BWB<F?kJQ<F32 FJL QM'2,((BWM1_ ImR K(F?HN( ~EwOMlH<F?H C+I(N B�~EL Q<F?H FJQ D FJB@2 ~EL Q<F?H � ��MOLmkJwOI ~EL Q wzy C/((wOMO{ ~EQWMlC+L K(F D FJB@2 FJB Fh4qA(wOMlkJMOQ<F32 FJL QQ<C+I(Q<F)( ~EwOMlH�F;C+I(N B�~EL Q<F � H^~EI D wlF0kc~+H�A ~EBWQWMlkJI(wOMlFJB K(F?H%RJwlR32 FJL Q<H�H�~ELmH�k?C+L Q<FJL I A C+I(B%wlF _ ImFJwlH�I(LmF�DGC+B@2 F~�((B<RJ{PR?F|Fh4 MlHWQ<F��mk?C/2L2 FxLmC+ImH;wlFxNPFJBWB<C+LmH;A(wOImH�wlC+MOL �h%

� ��l!GU��!�QM��IK�B� � ��/�RE - I(L5K(CqkJI�2 FJL Q � ^ j F?HWQ�K MOQH((MlFJL|DGC+B@2 R�Hay MOw B<F?HWA F?kJQ<F�Q<C+I(Q<F?HwlF?H;B 0J{fwlF?H0H@AqL Q�~F4 M1_ ImF?H0K y � ^ j %

c F A(wOImH�� ^ j A FJB@2 FJQ K(F K(Rh\mL(MOB K(F?HoQ�AqA F?HoK(F K(CqkJI�2 FJL Q<H % t L Q A A F K(F K(C kJI�2 FJL Q K(Rh\mL(MOQI(L k?FJBWQ�~EMOL LmC/2=((B<F|K(FxLmC/2 H;K y RJwlR32 FJL Q<Hv~EMOLmH<MO_ ImF3wlF|k?C+L Q<FJL I K(Fxk?F?H;RJwlR32 FJL Q<H � ~EI(QWB<F?H;RJwlR32 FJL Q<H��K(C+L(LmR?F?HvRJwlR32 FJL Q�~EMOB<F?H�� C+I H<R _ ImFJLmk?F|K(F|kc~EB�~+kJQ 0JB<F?H.LmC+L ~EL ~Ew'A H<R?F �h% <�F?H0Q�AqA F?H;K(F�K(C kJI�2 FJL Q<H.H<C+L QK(Rh\mL(MlH A ~EB k?F _ ImF wzy C+L ~EA(A FJwOwlF K(F?H c a c � � ��'�< �#&*>@58&> "�3 * ��* �J@�TA8UT '$@�� C+I FJLmk?C+B<F H<FJwlC+L'w ~LmC+B@2 F A(wOImH�B<R?k?FJL Q<F A ~EB K(F?H|H<k :mR32 ~+H � ^ j � � ^ j � nqk :mF32 ~ �h% f C+ImH|B<FJN MlFJLmK B<C+LmH HWI(B�k?F?H3DGC+B@2 F?HK(F|K(Rh\mL(MOQWMlC+L Km~ELmH0wlF?H;H<F?kJQWMlC+LmH;H<I(MON+~EL Q<F?H %

� ��l!GU��!�QM �� JI"nU� - I(L K(C kJI�2 FJL Q � ^ j F?HWQ K MOQ�N+~EwOMlK(F Hcy MOw�F?HWQ,((MlFJL�DGC+B@2 R FJQ Hay MOwB<F?H<A F?kJQ<Fxw ~oH<QWBWImkJQWI(B<F�K(Rh\mL(MlFxA ~EB0H^~ c a c C+I H�C+L H@:mR32 ~ %

j ~ HWQWBWImkJQWI(B<F K y I(L�K(CqkJI�2 FJL Q�� ^ j ((MlFJL DGC+B@2 RoHcy RJQ�~�((wOMOQ|k?C/2L2 F HWI(MOQ % a�C+I(Q|K(C kJI�2 FJL Q�k?C/2 �2 FJLmk?F A ~EB I(LmF A ~EBWQWMlF ~EA(A FJwlR?F 3�� '$)W'� ��* _ I(M�k?C+LmHWMlH<Q<F FJL�I(L FJLmH�F32,((wlF K(F K(R?kJw ~EB�~EQWMlC+LmH K(Fp( ~+H<FHWI(BvwlFoK(C kJI�2 FJL Q � A ~EB3Fh4(F32 A(wlF�� w ~ NPFJB<HWMlC+L#K y � ^ j FJQ3wlF)�WFJI#K(F5kc~EB�~+kJQ 0JB<F?H3I(QWMOwOMlH�R?H �h%tX LmHWI(MOQ<F�� wlFK(CqkJI�2 FJL Q;k?C/2 A C+BWQ<F.LmR?k?F?H�H�~EMOB<F32 FJL Q�I(L FJQ I(L H<FJI(w ~EB@((B<FvK y RJwlR32 FJL Q<H % j ~ H<QWBWImkJQWI(B<F3~EB@( C+B<F?H<k?FJL Q<FF?HWQxMOLmK I(MOQ<F A ~EB�wzy M'2,((BWMlkc~EQWMlC+L HWQWBWMlkJQ<F K(F?H|RJwlR32 FJL Q<H % j F5Dz~EMOQ,_ I y MOw�L y A ~EMOQ=_ I y I(L�H<FJI(w�~EB@((B<F Km~ELmH

-5%'$ j ~EL({ ~E{PF d ( ~EwOMlH<F?H;H<R32 ~EL QWM1_ ImF?H -5$

I(L�K(CqkJI�2 FJL QoF?HWQ|I(LmF B<F?H<QWBWMlkJQWMlC+L K y � ^ j % <�F?kJM%M'2 A(wOM1_ ImFp_ ImF wlF k?C+L Q<FJL I FJL�Q�~EL Q _ ImF Q<FJw%K y I(LK(CqkJI�2 FJL Q F?HWQ Q<C+I/�WC+I(B<HN( ~EwOMlH<R k?C/2L2 F I(L FJQ I(L H<FJI(w0RJwlR32 FJL Q � A C+I(N+~EL Qp((MlFJL H��(B FJL k?C+L Q<FJL(MOBA(wOImHWMlFJI(B<H �h%tX L5\mLM� I(L K(C kJI�2 FJL Q � ^ j A FJI(Q3k?C+L Q<FJL(MOB|K(F?H3k?C/2L2 FJL Q�~EMOB<F?H�� Km~ELmHvw ~p2 F?H<I(B<F C$;#C+LB<F?HWA F?kJQ<F A ~EB ~EMOwOwlFJI(B<HowlF?H5B 0J{fwlF?H H@AqL Q�~F4 M1_ ImF?H K y � ^ j % t L RJwlR32 FJL Q K(F k?C/2L2 FJL Q�~EMOB<F ~ w ~ DGC+B@2 FHWI(MONf~EL Q<F�,

�� j ~vK(R?kJw ~EB�~EQWMlC+L � ^ j K(R3((I(Q<F�wlF K(CqkJI�2 FJL Q %/X wOwlF�MOLmK M1_ ImF�~EI5A(B<C k?F?H�H<FJI(B)K(F K(CqkJI�2 FJL Q w ~0NPFJB<HWMlC+L

K y � ^ j I(QWMOwOMlH<R?F��mwlFb�WFJI K(F|kc~EB�~+kJQ 0JB<F?HvFJQ0wlFxDG~EMOQ�_ ImFxwlF|K(CqkJI�2 FJL Q3H<C+MOQ;MOL Q<FJBWA(B<RJQ�~�((wlF FJL wOI(My� 2��32 FC+I Hcy MOw�K(RJA FJLmK K y ~EI(QWB<F?H K(C kJI�2 FJL Q<H�� k?C/2L2 F I(LmF K(F?H�kJBWMOA(QWMlC+L K(F H�~ HWQWBWImkJQWI(B<F % j ~ DGC+B@2 F K(F w ~K(R?kJw ~EB�~EQWMlC+L � ^ j F?HWQ:,

� �m� � �5u&w�~B{(�/| � � � � u/|��*�&}�{`|!v � � �� ~J�5�/|B}B��/|�u �� 5u5~� �<�FJQWQ<F�( ~EwOMlH<FxF?HWQ�K y I(L Q�AqA FvH<A R?kJM ~Ew � MOL QWB<C K I(MOQ;A ~EB�wlFvA C+MOL Q;K y MOL Q<FJBWB<C+{ ~EQWMlC+L � FJQ�L y ~5A ~+Hb( F?H<C+MOL

K y �JQWB<F DGFJB@2 R?F % pswmHcy ~E{fMOQ%K y I(LmF ( ~EwOMlH<F0K y MOLmHWQWBWImkJQWMlC+L K(F�QWB�~EMOQ<F32 FJL Q�� H<I(B�wlF?H _ ImFJwOwlF?H�LmC+ImH�B<FJNqMlFJLmK B<C+LmHA(wOImH�wlC+MOL % j F%LmC/2 K(F�w ~)( ~EwOMlH<F%F?H<Q��&� � % j F?H LmC/2 H)k?C/2L2 F ��u/w�~B{(�&|vC+ILu/|��*�&}�{`|!vvH<C+L Q�K(F?H ~EQWQWBWM'((I(Q<H~+H<H<CqkJMlR?H d w ~,( ~EwOMlH<F % j F?H�k;: ~FElLmF?H FJL QWB<Fv{fI(MOwOwlF32 FJQ<H�H<C+L Q�wlF?H�N+~EwlFJI(B<H K(Fvk?F?H�~EQWQWBWM'((I(Q<H % a�C+I(Q<F0Nf~EwlFJI(BK y ~EQWQWBWM'((I(Q.K(C+MOQ �JQWB<FxA(w ~+k?R?F|FJL QWB<F|{fI(MOwOwlF32 FJQ<H.C+I FJL QWB<F ~EA CfHWQWB<C+A�:mF?H %

[ A(B 0?H)w ~vK(R?kJw ~EB�~EQWMlC+L � ^ j ~EI K(R3((I(Q�K IoK(CqkJI�2 FJL Q��+wlF�A(B<C+wlC+{fImF A FJI(Q k?C+L Q<FJL(MOB�I(LmF K(R?kJw ~EB�~EQWMlC+LK(F Q A A F K(F K(C kJI�2 FJL Q % <�FJQWQ<F K(R?kJw ~EB�~EQWMlC+L'K(C+L(LmF I(L LmC/2 ~EI Q�AqA F K(F K(CqkJI�2 FJL QoFJQ K(R?kJw ~EB<F wlF?HRJwlR32 FJL Q<H|A C+I(Nf~EL Q|~EA(A ~EB�~FElQWB<F Km~ELmH3wlFoK(C kJI�2 FJL Q|K(F,2��32 FL_ ImF wlFJI(BvM'2=((BWMlkc~EQWMlC+L�B<F?HWA F?kJQWMONPF % j ~DGC+B@2 F|K(Fxk?FJQWQ<F|K(R?kJw ~EB�~EQWMlC+L F?H<Q:,

�� w5�/x!x �&w�� 6RP<9)02�� 2�8UT '$@ � �f C+ImHxNPFJBWB<C+LmH�FJL�K(RJQ�~EMOw�w ~ A ~EBWQWMlF �EK(R?kJw ~EB�~EQWMlC+LmH �#wlC+B<H _ ImFoLmC+ImH�K(R?kJBWMOB<C+LmH|wlF?H c a c d w ~ A(B<C��

k : ~EMOLmF H�F?kJQWMlC+L %T[ A(B 0?H k?FJQWQ<F K(R?kJw ~EB�~EQWMlC+L K(F Q�AqA F K(F K(CqkJI�2 FJL Q��C+L QWB<C+I(NPF wzy ~EB@((B<F K y RJwlR32 FJL Q<H��K(C+Lmk3wlF3k?C+L Q<FJL I k?C/2L2 F3Q<FJw K I K(CqkJI�2 FJL Q�A(w ~+k?R|FJL QWB<F3I(LmF3A ~EMOB<FxK(F�( ~EwOMlH<F3C+I(N B�~EL Q<F|FJQ�D FJB@2 ~EL Q<FK(C+L Q3wlF�LmC/2�K y RJwlR32 FJL Q<HxF?HWQ0wlF LmC/2�K(F�Q�AqA F5K(F5K(C kJI�2 FJL Q3~EA(A ~EB�~EMlH<H^~EL QxKm~ELmHvw ~ K(R?kJw ~EB�~EQWMlC+L�K(FQ�AqA FxK(F|K(C kJI�2 FJL Q � Km~ELmH�LmC+QWB<F�Fh4 F32 A(wlF�� k?FxH<FJB�~EMOQ)w5�&x�x'�/w�� h%j F?H0kJBWMOQ 0JB<F?H _ I(M DGC+L Q�_ I y I(L K(CqkJI�2 FJL Q � ^ j F?HWQ ((MlFJL DGC+B@2 R|H<C+L Q!,� B<F?HWA F?kJQ;K(F?H�B 0J{fwlF?H0K(FxLmC/2L2 ~E{PF�K(F?H;RJwlR32 FJL Q<H � ( ~EwOMlH<F?H � �� B<F?HWA F?kJQ.K I A ~EMOB�~E{PF5FJL QWB<F,( ~EwOMlH�F?HvC+I(NqB�~EL Q<F?H3FJQ.D FJB@2 ~EL Q<F?H � 2 C K I(wlC wlF?H ( ~EwOMlH<F?H.H<A R?kJM ~EwlF?HvLmFLmR?k?F?H<HWMOQ�~EL Q;A ~+H0K(FvDGFJB@2 FJQWI(B<F � �� B<F?HWA F?kJQ;K(Fxwzy M'2,((BWMlkc~EQWMlC+L HWQWBWMlkJQ<FxK(F?H)( ~EwOMlH�F?H��(FJQ� B<F?HWA F?kJQ;K(Fxwzy I(L(MlkJMOQ<R|K(Fxwzy ~EB@((B<F|K y RJwlR32 FJL Q<H;DGC+B@2 ~EL Q.wlFxk?C+L Q<FJL I K I K(CqkJI�2 FJL Q %j F?H+( ~EwOMlH<F?H|K(Rh\mL(MlF?H|A ~EB|wlF kJB<Rc~EQ<FJI(B�K I�K(CqkJI�2 FJL Q � C+I#A(wOImHxwlC+MOL�K(F w ~ c a c C+I�K I�H<k;:mR32 ~ �

A FJI(NPFJL Q��k?C/2L2 F wlF?H ( ~EwOMlH<F?HoA(B<R?K(Rh\mL(MlF?H�� A C+BWQ<FJB5K(F?H ~EQWQWBWM'((I(Q<H % j F?H ~EQWQWBWM'((I(Q<H H�C+L QoA(w ~+k?R?H Km~ELmHw ~ ( ~EwOMlH<F�C+I(N B�~EL Q<F�K y I(L RJwlR32 FJL Q %�. ~EB.Fh4(F32 A(wlF��mw ~ ( ~EwOMlH�F|C+I(N B�~EL Q<F*w��/x�x'�/w�� K(FxLmC+QWB<F�K(C kJI�2 FJL QA(B<R?k?R?K(FJL Q.A C+I(BWB�~EMOQ.H<F3A(B<R?H<FJL Q<FJBvK(Fxw ~ 2 ~EL(M10JB<F�H<I(MON+~EL Q<F�,

� w5�&x�x'�/w�� !�/|!v�)5u � ��}B�*�5u �3� �m}�{�z � � �B� � � � � � � � R}�{Fz!z )�~B{(�&| � &�(�&|!z�{�}Bu&|��{&u�� j F?H LmC/2 H K y ~EQWQWBWM'((I(Q<H B<F?HWA F?kJQ<FJL Q K(F?H B 0J{fwlF?H K(F k?C+LmHWQWBWImkJQWMlC+L MlK(FJL QWM1_ ImF?H d k?FJwOwlF?H K(F?H LmC/2 H

K y RJwlR32 FJL Q<H %

� qO�!�Rk� "� # �1D j F K(CqkJI�2 FJL Q � ^ j HWI(MONf~EL QxLmF k?C/2 A C+BWQ<FoA ~+HxK(FoK(R?kJw ~EB�~EQWMlC+L�K(FoQ�AqA F5K(F K(CqkJI5�2 FJL Q�� MOw�F?HWQ.K(C+Lmk+((MlFJL DGC+B@2 R|H�~ELmH0A C+I(NPC+MOBvk?FJA FJLmKm~EL Q �JQWB<FxNf~EwOMlK(R % psw k?C+L QWMlFJL QxK(F?H;MOL DGC+B@2 ~EQWMlC+LmHHWI(B�I(L A ~EB<k�K y C+B<K MOL ~EQ<FJI(B<H.K y I(LmF|FJL QWB<FJA(BWMlH<F %� �&� � ��u/w�~!{(�&| �� u/|��(�m}�{`|Bv �� !� � ~��5�&|!}5��&|5u � ��uB~ �� &w!}�{`|5�*�5u*)�w�~ �

- � j Fxw ~EL({ ~E{PF�� ^ j

� ��5�!��{`|�u �� | �� {`|��")�|�{ � �D)�+�~>� zmw � �/|'�F� �� | � ��u*��5u&w�|�u(� � � � � � � � � � �� /|'�!�/u(��u/w!|5u(� �� | � �m{Fx � � �� "� � � �B� � � � �&| �!��{`x �� }B�*�5u �3�Q{�~&u ��u/| �&~mu/w��{��&u � � � �� &}5�(�5u �3�t{m~&u ��u&|��&~mu/w��{��&u �� !x5u �&~"��~��uF��u �� {`|!} �J$�~ �� *��!x5u!�m~"��~��5u��u �� {`|�~��!�(��u()�w �� u��/|��Bu � w5u(�'�/| � �5{F|�~J�5��*�5u()!w �

� ��5��{F|5u �� 5�!��{`|�u �

� | �� w5u5�&u/|�� ")!|�{"��D) +�~H��zmw � �&| �F� �� | � ��u*��5u&w�|�u(� � � � � � � �� "� � � �/|'�!�/u(��u/w!|5u(� �� | � �m{Fx � � � �B� � � � � � �� &| �!��{`x �� }B�*�5u �3�Q{�~&u ��u/| �&~mu/w��{��&u � � � �� -� � � �� &}5�(�5u �3�t{m~&u ��u&|��&~mu/w��{��&u �� !x5u �&~"��~��uF��u � ��{`|�)�� u&}��5�(��B� �"� �(��x5u �&~ ��~��uF��u �� {`|�~��!�(��u()�w � � {!� �*)5�&|�5u � {`|�)��{&u()�� {`|�~��5��!�(�5u*)�w �

� ��5��{F|5u �� /wB}�{`|��(��u()�w�~ �

2

� �� 4�6 # 4 # � /�2 !�4�=.@ 684)@� �

j F?HxK(C kJI�2 FJL Q<H � ^ j N+~EwOMlK(F?H3C/( RJMlH<H<FJL Q d K(F?HvB 0J{fwlF?H3K(Fok?C+LmHWQWBWImkJQWMlC+L#A(B<R?kJMlH<F?H�� kfy F?HWQ � d � K MOB<F dI(L�Q A A F K(F K(C kJI�2 FJL Q<H % � ^ j A(B<C+A CfH�F K(FJI54 2 CPAPFJLmH5A C+I(B�K(Rh\mL(MOB5K(F?H�Q�AqA F?H K(F K(CqkJI�2 FJL Q % j FA(wOImH�~ELmkJMlFJL FJQ wlF A(wOImH�HWM'2 A(wlF F?HWQ w ~ c a c C+I � ��'�< �#�*9@58 >�"�3 *��* �J@�TA8UT '$@�� %/. wOImH B<R?k?F32L2 FJL Q��fI(LmFLmC+I(NPFJwOwlFxDGC+B@2 FxK(F|K(Rh\mL(MOQWMlC+L F?HWQ0~EA(A ~EBWImF ~cNPF?kxwlF?H;H<k;:mR32 ~+H��mC+I FJLmk?C+B<F � �� <>4H*>#�2 9��_ I(M H<C+L QI(LmF|Fh4 Q<FJLmHWMlC+L K(F?H c a c A FJB@2 FJQWQ�~EL Q0I(LmFxK(Rh\mL(MOQWMlC+L A(wOImH�A(B<R?kJMlH<F % c a c FJQ0H<k;:mR32 ~+H0K(C+MONPFJL Q �JQWB<FK(Rh\mL(MlF?H5FJL�I(QWMOwOMlH�~EL Q5I(L�k?FJBWQ�~EMOL w ~EL({ ~E{PF % � L ~EI(B�~EMOQ�A(I�k;:mC+MlHWMOB L y M'2 A C+BWQ<Fp_ ImFJwOwlF H@AqL Q�~F4(F A C+I(Bk?F Dz~EMOB<F��U2 ~EMlH � ^ j RJQ�~EL Q5wOI(My� 2��32 F I(L�w ~EL({ ~E{PF Fh4 Q<FJLmHWM'((wlF A ~EBoK(Rh\mL(MOQWMlC+L'K(F LmC+I(NPFc~EI54�Q A A F?HK(F K(C kJI�2 FJL Q<H��C+L ~ k :mC+MlHWM�K(F K(Rh\mL(MOB wlF?H c a c FJQ5wlF?H H<k :mR32 ~+H k?C/2L2 F K(F?H K(CqkJI�2 FJL Q<H�� ^ j �A CfH<H<R?Km~EL Q.K(C+LmkxwlFJI(B<H�A(B<C+A(B<F?H;Q A A F?H;K(F|K(CqkJI�2 FJL Q<H��mFJQ0K(C+LmkxwlFJI(B<H�A(B<C+A(B<F?H0Q�AqA F?H0K y RJwlR32 FJL Q<H %t LmF c a c K(Rh\mL(MOQ�wlF?H�Q�AqA F?H�K y RJwlR32 FJL Q<H��mK(C+Lmk3wlF?H LmC/2 H;K(F ( ~EwOMlH<F?H�� wlF.Q A A FxK(FvwlFJI(B;k?C+L Q<FJL I FJQ

wzy C+BW{ ~EL(MlH�~EQWMlC+L K(F?H;Q�AqA F?H;K y RJwlR32 FJL Q<H;wlF?H�I(LmH A ~EB�B�~EA(A C+BWQ.~EI54 ~EI(QWB<F?H %�. ~EB0C+BW{ ~EL(MlH�~EQWMlC+L 2 I(QWImFJwOwlFK(F?H Q�AqA F?H)K y RJwlR32 FJL Q<H��PC+L FJL Q<FJLmKowzy MOLmkJwOImH<MlC+L K(F%Q A A F?H�K y RJwlF32 FJL Q<H�Km~ELmH�K y ~EI(QWB<F?H�Q�AqA F?H K y RJwlR32 FJL Q<H��A k?C/2 A(BWMlH;w ~ 2�I(wOQWMOA(wOMlkJMOQ<R5RJNPFJL QWImFJwOwlF K(F?H0RJwlR32 FJL Q<H;A C+I(N+~EL Q.~EA(A ~EB�~FElQWB<F�Km~ELmH.K y ~EI(QWB<F?H0RJwlR32 FJL Q<H %j ~ c a c F?HWQ�MOL QWB<CqK I(MOQ<F;A ~EB%w ~xK(R?kJw ~EB�~EQWMlC+L �� Km~ELmH�wlF A(B<C+wlC+{fImF.K I K(CqkJI�2 FJL Q % j ~xK(R?kJw ~F�

B�~EQWMlC+L � � � �� K(Rh\mL(MOQ d w ~0D C+MlH wlF LmC/2 K I Q A A F�K(F K(C kJI�2 FJL Q�~EI�_ ImFJwmC/( RJMOQ wlF�K(CqkJI�2 FJL Q%k?C+I(B�~EL Q��A(I(MlH MOL QWB<CqK I(MOQ�wlF?H�K(R?kJw ~EB�~EQWMlC+LmH�K y C+BW{ ~EL(MlH�~EQWMlC+L A(B<C+A(B<F?H d k?F�Q�AqA F K(F�K(CqkJI�2 FJL Q<H % <�F?H�K(R?kJw ~EB�~EQWMlC+LmHK y C+BW{ ~EL(MlH�~EQWMlC+L'H<F A(B<R?H<FJL Q<FJL Q H<C+ImH�I(LmF DGC+B@2 F�_ I(M%B<F?H<H�F32,((wlF�( Fc~EImk?C+I(A d I(LmF {fB�~�2L2 ~EMOB<F LmC+L5�k?C+L Q<Fh4 QWImFJwOwlF %�X L DG~EMOQ�� wlF w ~EL({ ~E{PF K(F K(Rh\mL(MOQWMlC+L'K(F w ~ {fB�~�2L2 ~EMOB<F K I K(C kJI�2 FJL Q F?HWQ�wlRJ{m0JB<F32 FJL QRJQ<FJLmK IoA C+I(B)MOLmkJwOI(B<F K(F?H k?C+LmHWQWBWImkJQWMlC+LmH�K(F%{fB�~�2L2 ~EMOB<F?H X } f.u � � �8S*>@�� *�� 2 < ��6 � �!2 ��M' �># � �h%. C+I(B0k : ~/_ ImF|RJwlR32 FJL Q0MOL QWB<CqK I(MOQ;A ~EB;H<C+L LmC/21� w ~oK(R?kJw ~EB�~EQWMlC+L K(C+L(LmFxwlF3k?C+L Q<FJL I K(F3wzy RJwlR32 FJL Q;A ~EBH<C+L'Q A A F K(F K(C+L(LmR?F?H A(B<R?K(Rh\mL(MlF?H C+I'A ~EB wlF?H LmC/2 H K y RJwlR32 FJL Q<H A C+I(N+~EL QLA ~EA(A ~EB�~FElQWB<F % j y C+B<K B<FFJQvw ~N2 I(wOQWMOA(wOMlkJMOQ<R K(F?H.RJwlF32 FJL Q<HxKm~ELmHvk?FJQWQ<F5K(R?kJw ~EB�~EQWMlC+L�F?HWQvHWMO{fL(My\ kc~EQWMONPF�� k?C/2L2 F Km~ELmHvI(LmF B 0J{fwlFK(FxA(B<CqK ImkJQWMlC+L K y I(LmF�{fB�~�2L2 ~EMOB<F %�. ~EBv~EMOwOwlFJI(B<H��mw ~ K(R?kJw ~EB�~EQWMlC+L K y I(L RJwlR32 FJL QvMOLmkJwOI(Q.RJ{ ~EwlF32 FJL Qvw ~K(Rh\mL(MOQWMlC+L K(F?H�~EQWQWBWM'((I(Q<H _ ImF.wzy C+L A C+I(BWB�~�QWB<C+I(NPFJB Km~ELmH�w ~,( ~EwOMlH<F3C+I(N B�~EL Q<F3K(F0wzy RJwlR32 FJL Q��m~EQWQWBWM'((I(Q<HK(Rh\mL(MlH;A ~EB�wlFJI(B<H0LmC/2 H;FJQ;wlF?H�Q A A F?H;K(FxwlFJI(B;k?C+L Q<FJL I %

-5% � a A A F?H;K(FxK(CqkJI�2 FJL Q<HvFJQ c a c -&7

� qO�!�Rk� "� # �'i <�C+LmHWMlK(RJB<C+LmH K y ~�( C+B<K wlF A(B<C+wlC+{fImF K y I(L K(CqkJI�2 FJL Q k?C+L Q<FJL ~EL Q I(L H�FJI(wvRJwlR32 FJL QLmC/2L2 R)u(��uF�Bx!��uvK(C+L Q)wlF�k?C+L Q<FJL I H<FJB�~.HWM'2 A(wlF32 FJL Q�K IoQ<Fh4qQ<F�A(I(B k?C+LmHWMlK(RJB<R k?C/2L2 F�LmC+L5� H<QWBWImkJQWI(B<R %j FxA(B<C+wlC+{fImF�H<FJB�~ ~EwlC+B<H:,

� �m� � �5u&w�~B{(�/| � � � � �u&|��*�&}�{F|!v � �� o~J�5�/|B}B��/|�u �� 5u5~� �� u(�5u��Bx!��u �

� � � � �� u*�5uF�5x��!u ( � � � � � � � - �� u(��uF�5x��u � � u5��{ u5~��)�| u(��uF�Bx!��u }Bu } �5�!)m��u&|�� !u(��uF�Bx!��u �

<�FJQ Fh4 QWB�~EMOQ D C+B@2 F I(L K(CqkJI�2 FJL Q � ^ j k?C/2 A(wlFJQ��U((MlFJL�DGC+B@2 R FJQ�Nf~EwOMlK(F % j ~ ( ~EwOMlH<F � � �� Dz~EMOQA ~EBWQWMlF3K I w ~EL({ ~E{PFxK(FvK(Rh\mL(MOQWMlC+L K(F?H c a c %BX wOwlFvMOL QWB<CqK I(MOQ w ~5K(Rh\mL(MOQWMlC+L K y I(L RJwlR32 FJL Q;FJL K(C+L(L ~EL QH<C+L LmC/2 � MlkJMUu*�5uF�5x��!u � A(I(MlH;H<C+L k?C+L Q<FJL I FJL QWB<FxA ~EB<FJL Q@:�0?H�F?H � MlkJM HWM'2 A(wlF32 FJL Q;wlF3Q�AqA FxK(FxK(C+L(LmR?F?HK(F ( ~+H<F � � � � � � �Q�%kfy F?HWQ � d � K MOB<F �)� 2��7 �*�� 42 �(2 < 8S* � � � > �� Km~ELmH wlF w ~EL({ ~E{PF K(F K(Rh\mL(MOQWMlC+L K(F?Hc a c �h%

2

t LmF c a c A FJI(Q �JQWB<FoMOL QWB<CqK I(MOQ<F Km~ELmH3w ~ K(R?kJw ~EB�~EQWMlC+L � � � �� TA@. >TA8 �#C+I#FJLmk?C+B<F �JQWB<F K(Rh\mL(MlFKm~ELmH�I(L K(CqkJI�2 FJL Q d A ~EBWQH_ I(MqF?HWQ B<RiDGRJB<FJLmk?R�Km~ELmH�w ~;K(R?kJw ~EB�~EQWMlC+L �� % n I(A(A CfH<C+LmH�A ~EB�Fh4(F32 A(wlF_ ImF�w ~ c a c K IoK(CqkJI�2 FJL Q Fh4 F32 A(wlF�A(B<R?k?R?K(FJL Q�H<C+MOQ)K(Rh\mL(MlF�Km~ELmH�I(L K(CqkJI�2 FJL Q u(��uF�5x��u ��}��!}5�E~EwlC+B<Hw ~oK(R?kJw ~EB�~EQWMlC+L � � � �� H<I(MON+~EL Q<FxN+~ Dz~EMOB<F3B<RiDGRJB<FJLmk?F d k?FJQWQ<F c a c Fh4qQ<FJBWLmF&,

�� u(�5u��Bx!��u � �� @u(��uF�5x��u ��}��!}�� c ~ELmH�k?F%kc~+H��aC+L HWI(A(A CfH<F _ ImF�wlFT\ k;:(MlFJBTu*�5u��Bx��!u�� } �!}.F?HWQ�k?C+wlCqkc~EwOMlH<R�~?NPF?k�wlFT\ k :(MlFJB u(�5u��Bx!��u��&� �

k?C+L Q<FJL ~EL Q|wlF5K(C kJI�2 FJL Q3Fh4(F32 A(wlF5A(B<R?k?R?K(FJL Q % � ^ j K(Rh\mL(MOQxK(F?H 2 CPAPFJLmH3A C+I(BvB<RiD RJB<FJB d K(F?H c a cHWMOQWImR?F?H�Km~ELmH�K(F?H ((M'((wOMlC+Q@:�0 _ ImF?H K(F c a c �!2 CPAPFJLmH _ ImF0LmC+ImH%LmF0NPFJBWB<C+LmH�A ~+H�MlkJM � k?C+LmH<I(wOQ<F�� ^ Mlk Z5$ �A C+I(B�A(wOImH%K(F�K(RJQ�~EMOwlH%H<I(B�wlF?H�I(QWMOwOMlH�~EQWMlC+LmH%A(B�~EQWM1_ ImF?H�K(F�� ^ j �h% c F�A(wOImH��+wlC+B<H _ I y I(L K(CqkJI�2 FJL Q � ^ jI(QWMOwOMlH<F I(LmF c a c Fh4qQ<FJBWLmF��MOw�L y F?HWQoA(wOImH MOL Q<FJBWA(B<RJQ�~�((wlF K(F 2 ~EL(M10JB<F MOLmK(RJA FJLmKm~EL Q<F �%MOw�Dz~EI(Q K(C+Lmk2 CqK My\ FJB�w ~3K(R?kJw ~EB�~EQWMlC+L �m� �3A C+I(B�B<R>O RJQ<FJB�k?FJw ~3FJL k : ~EL({PFc~EL Q�w ~3Nf~EwlFJI(B�K(F�wzy ~EQWQWBWM'((I(Q ~��/|B}B��/|�u ,

� �m� � �5u&w�~B{(�/| � � � � u/|��*�&}�{`|!v � � �� ~J�5�/|B}B��/|�u ��3| ��

�"��

j ~ c a c k?C+L QWMlFJL Q�K y ~�( C+B<K w ~3K(R?kJw ~EB�~EQWMlC+L K(F?H�RJwlR32 FJL Q<H�K I Q�AqA F�K(F�K(CqkJI�2 FJL Q<H % <�FJQWQ<F;K(R?kJw ~EB�~F�QWMlC+LM�(k?C/2L2 FxLmC+ImH wzy ~cNPC+LmH;NqIM�qF?H<Q DG~EMOQ<F3A ~EB I(LmF�( ~EwOMlH<FxHWA R?kJM ~EwlF � � �� K(C+L Q;w ~ DGC+B@2 F3{PRJLmRJB�~EwlFF?HWQ:,

�� @Q'$# #�'�� 9)W* �C$;.@Q'$# F?H<Q�wlF3LmC/2 K(F3wzy RJwlR32 FJL Q.K(Rh\mL(M FJQ #�'�� 9)W* Fh4 A(wOMlkJMOQ<F3wlFxk?C+L Q<FJL I K(F3wzy RJwlR32 FJL Q % j Fxk?C+L Q<FJL IK(F3wzy RJwlR32 FJL Q.F?HWQ I(LmF3wOMlHWQ<FxK y RJwlR32 FJL Q<H)\mwlH�C+I K(F3Q�AqA F?H�K(FxK(C+L(LmR?F?H�A(B<R?K(Rh\mL(MlH��mC+I FJLmk?C+B<F3wzy I(L K(F?H2 C+Q<H � kJwlR?H � �� C+I �� ,� j F?H�RJwlR32 FJL Q<H>\mwlH�H�C+L Q�H<M'2 A(wlF32 FJL Q MOL QWB<CqK I(MOQ<H�A ~EB%wlFJI(B<H�LmC/2 H % n M wlF?H%LmC/2 H�K(F?H�RJwlR32 FJL Q<H>\mwlHH<C+L Q H<RJA ~EB<R?H�A ~EB K(F?H�NqMOBW{fI(wlF?H�~EwlC+B<H�wzy C+B<K B<FvKm~ELmH�wlF _ ImFJw wlF?H RJwlR32 FJL Q<H \mwlH�K(C+MONPFJL Q;~EA(A ~EB�~FElQWB<FF?HWQ M'2 A CfH<R�� . ~EB k?C+L QWB<F��HWM.C+L wlF?H H<RJA ~EB<F A ~EB K(F?HN( ~EBWB<F?H NPFJBWQWMlkc~EwlF?H ~EwlC+B<H MOw.Hay ~E{fMOQ K y I(LmF~EwOQ<FJBWL ~EQWMONPF��mI(L RJwlR32 FJL Q0A ~EB@2 M wlF?H.~EwOQ<FJBWL ~EQWMONPF?H0K(FJNf~EL Qv~EA(A ~EB�~FElQWB<F %

� j F?H3RJwlR32 FJL Q<H3DGFJI(MOwOwlF?HxC+I wlF?HxRJwlR32 FJL Q<H�2 My4 Q<F?H � ~?NPF?k RJwlR32 FJL Q<H \mwlHxFJQ3K(F?HxK(C+L(LmR?F?HxK(F ( ~+H<F �A FJI(NPFJL Q�k?C+L Q<FJL(MOB�F?H<H�FJL QWMlFJwOwlF32 FJL Q�I(L�O �+Q�K(F;kc~EB�~+kJQ 0JB<F?H�K(C+L Q�wlF;Q�AqA F�A(B<R?K(Rh\mL(M F?HWQ�� %c ~ELmH�I(L Q<FJw k?C+L Q<FJL I A FJI(NPFJL Q3~EA(A ~EB�~FElQWB<F|Q<C+ImH.kc~EB�~+kJQ 0JB<F?H0H�~EI D wlF?H0kc~EB�~+kJQ 0JB<F?H y � y � _ I(M MOLmK My�_ ImFJB�~EMOQ�wlF3K(R3((I(Q�K(F0w ~,( ~EwOMlH<F.D FJB@2 ~EL Q<F � FJQ�wlF5y � y % c F?H R?k : ~EA(A F32 FJL Q<H0H�C+L Q�A(B<RJN ImH�wlC+B<H _ I y C+LK(C+MOQ I(QWMOwOMlH�FJB k?F?H kc~EB�~+kJQ 0JB<F?H % c y ~EI(QWB<F?H Q A A F?H K(F k?C+L Q<FJL ImH H<C+L Q A CfH<HWM'((wlF?H��%FJL I(QWMOwOMlH�~EL Q w ~LmC+QWMlC+L K(F @Q' 8 2�8UTU'�@ _ ImF3LmC+ImH;LmF3NPFJBWB<C+LmH;A ~+H;MlkJM %

-�] j Fxw ~EL({ ~E{PF�� ^ j

� j Fb2 C+Q � kJwlR � �� A FJB@2 FJQ�K(F�K(Rh\mL(MOB�I(L RJwlR32 FJL Q�K(C+L Q�wlF�k?C+L Q<FJL I F?H<Q)wOM'((B<F � Aok?C/2 A(BWMlH%~cNPF?k;K(F?H( ~EwOMlH<F?HvMOL Q<FJBWLmF?H �h% <�F5Q A A FoK y RJwlR32 FJL Q<H|F?HWQ3A ~EBWQWMlkJI(wOM10JB<F32 FJL Q|I(QWMOwlF Km~ELmHvwlF?H3A�: ~+H<F?HvMOL(MOQWM ~EwlF?HK(F K(Rh\mL(MOQWMlC+L K y I(LmF c a c A C+I(B5B<F?k?C+L(L ~FElQWB<F K(F?H K(C kJI�2 FJL Q<H Fh4qMlH<Q�~EL Q<H 2 ~EMlH K(C+L Q wlF Q A A FL y F?HWQ�A ~+H;FJLmk?C+B<F k?C/2 A(w10JQ<F32 FJL Q3K(Rh\mL(M %

� j F+2 C+Q � kJwlR �� A FJB@2 FJQvK(F|K(Rh\mL(MOB3K(F?H0RJwlR32 FJL Q<HvK(C+L Q.wlF|k?C+L Q<FJL I#H<FJB�~oQ<C+I/�WC+I(B<H;NqMlK(F % <�F{PFJL(B<F K y RJwlR32 FJL Q<H A C+BWQ<F LmC+B@2 ~EwlF32 FJL Q K(F?H ~EQWQWBWM'((I(Q<H�_ I(M�wOI(M.K(C+L(LmFJL Q I(L B��+wlF A ~EBWQWMlkJI(wOMlFJBKm~ELmH�I(L K(CqkJI�2 FJL Q %

� L A FJI(Q I(QWMOwOMlH<FJB Km~ELmH w ~ K(Rh\mL(MOQWMlC+L8K(F?H RJwlR32 FJL Q<H \mwlH K(F?H C+A RJB�~EQ<FJI(B<H K y C k?kJI(BWB<FJLmk?F#C+I�K(F2�I(wOQWMOA(wOMlkJMOQ<R5QWB 0?HvHWM'2 MOw ~EMOB<F d k?F=_ ImF�wzy C+L B<FJLmk?C+L QWB<FoKm~ELmHvwlF?H0Fh4 A(B<F?H<HWMlC+LmH.B<RJ{fI(wOM10JB<F?H , y ymMOLmK M1_ ImFwzy C+A(QWMlC+L(L ~EwOMOQ<R��)y � y(MOLmK M1_ ImFxw ~oB<RJA RJQ�~�((MOwOMOQ<R�C+A(QWMlC+L(LmFJwOwlF�� ~EwlC+B<H�_ ImF y � y(MOLmK M1_ ImFxw ~oB<RJA RJQ�~�((MOwOMOQ<R ~cNPF?kA(B<R?H<FJLmk?F K y ~EI�2 C+MOLmH|I(LmF Cqk?kJI(B<FJLmk?F % j F?H|A ~EB<FJL Q@:�0?H<F?H A FJI(NPFJL Q��JQWB<F I(QWMOwOMlH�R?F?HxA C+I(B K(RJwOM'2 MOQ<FJB�w ~A C+BWQ<R?F|K(F?H;C+A RJB�~EQ<FJI(B<H0K y Cqk?kJI(BWB<FJLmk?F % c ~ELmH�wlF?H;K(Rh\mL(MOQWMlC+LmH ,

�� ~&u��!��{*�/| (1��{!�!w5u!�m~&u��!��{*�/| � �*�/w�x�~ �m~&u5��{*�/| - �� !��/x�{��w�u ( ��{��w5u � {F|��!w � � ~mu5�!��{(�&| � - �

C+LoMOLmK M1_ ImF _ I y I(LmF H<F?kJQWMlC+L k?C/2 A C+BWQ<F I(L5QWMOQWB<F�FJQ I(L k?C+BWAmH��P~EwlC+B<HT_ I y I(L k : ~EA(MOQWB<F;F?HWQ�k?C/2 A CfH<R K y I(LQWMOQWB<F��qK y I(LmF0MOL QWB<C K ImkJQWMlC+L FJQ�K y ~EI�2 C+MOLmH�I(LmFvH<F?kJQWMlC+L % <�C/2L2 F3K(R � d 2 FJL QWMlC+L(LmR�� w ~+( ~EBWB<FvNPFJBWQWMlkc~EwlFy�*Wy MOL QWB<C K I(MOQ.I(LmF�~EwOQ<FJBWL ~EQWMONPF % c ~ELmH�w ~ K(Rh\mL(MOQWMlC+L ,

�� (�&w�x�~��&~mu5�!��{(�&| ( � � � � � � � * +�{ +!w5umz - � �

C+L MOLmK M1_ ImF _ ImF�wlF k?C+BWAmHvK y I(LmF H�F?kJQWMlC+L F?HWQ.I(LmF�B<RJA RJQWMOQWMlC+L K(F Z � $ C+I A(wOImH<MlFJI(B<HvCqk?kJI(BWB<FJLmk?F?H3H<C+MOQK y I(LmFvH<R _ ImFJLmk?F.K(F0kc~EB�~+kJQ 0JB<F?Hb_ ImFJwlk?C+L�_ ImF?H � H�~EI D�y � y FJQ.y � y � C+I K y I(L RJwlR32 FJL Q +�{�+�w5umz5� kfy F?HWQ � d � K MOB<FI(LmFxB<RiDGRJB<FJLmk?F+((M'((wOMlC+{fB�~EA�:(M1_ ImF %

<>: ~/_ ImF RJwlR32 FJL Q A FJI(Q ~?NPC+MOB Z ��I(L C+I A(wOImH<MlFJI(B<H ~EQWQWBWM'((I(Q<H % j ~ K(R?kJw ~EB�~EQWMlC+L�K y ~EQWQWBWM'((I(Q<H Dz~EMOQMOL Q<FJBWNPFJL(MOBvwlF3LmC/2 K(F|wzy RJwlR32 FJL Qv~EI�_ ImFJw wzy ~EQWQWBWM'((I(QvF?HWQ;B�~EQWQ�~+k :mR�� wlFxLmC/2�K(Fxwzy ~EQWQWBWM'((I(Q�� wlFxQ�AqA F|K(F?HNf~EwlFJI(B<H�K(F wzy ~EQWQWBWM'((I(Q�FJQ�I(LmF�MOLmK Mlkc~EQWMlC+L K(F�N+~EwlFJI(B�A ~EB�K(RiDG~EI(Q % j F?H�~EQWQWBWM'((I(Q<H%~+H<H<CqkJMlR?H d I(L RJwlR32 FJL QH<F3B<FJ{fB<C+I(A FJL QvKm~ELmH�I(LmFxwOMlHWQ<FxMOL QWB<C K I(MOQ<F|A ~EB;w ~ ( ~EwOMlH<F � �� ,

�� @Q'$# � R>)+R>#&*>@58 @B'$# � 2�8 8 �>T % �8 8U"�3 * � 2�8 8 ��T %��H8 �6R � 2 �H8 �j FxLmC/2 K y RJwlR32 FJL Q3K(C+MOQ�B<RiDGRJB<FJB d I(L RJwlR32 FJL Q.Fh4qMlHWQ�~EL Q0Km~ELmH;w ~ c a c % j FxLmC/2 K y ~EQWQWBWM'((I(Q0K(C+MOQ

B<F?HWA F?kJQ<FJB�wlF?H 2��32 F?H�B 0J{fwlF?H�H@AqL Q�~F4 M1_ ImF?H _ ImFvwlF?H LmC/2 H;K y RJwlR32 FJL Q<H % j FvQ�AqA F3K y ~EQWQWBWM'((I(Q0F?HWQ�k;:mC+MlHWM �FJL QWB<F5~EI(QWB<F?H�� A ~EB@2 M wlF?H;Q�AqA F?H;H<I(MON+~EL Q<H:,

� � � � � - k;: ~FElLmF�K(Fxkc~EB�~+kJQ 0JB<F?H�� QG � � � � - B<FJL NPC+MlH d wzy MOL Q<RJBWMlFJI(B3K I K(C kJI�2 FJL Q�� G � �� - FJL QWMOQ<R?H.Fh4qQ<FJBWLmF?H d � ^ j �� QG � � � �� - MlK(FJL QWMy\ kc~EQ<FJI(B<H.C+I Nf~EwlFJI(B<H;H@AB2,( C+wOM1_ ImF?H�� - K(C+L(LmR?F?H;MOL Q<FJBWA(B<RJQ�~�((wlF?H.A ~EB;I(L C+I(QWMOw�Fh4qQ<FJBWLmF d � ^ j � M'2 ~E{PF?H��mH<C+LmH��(FJQ<k % � � "I"� MP� nU� l U��IKq - K(F w ~ D C+B@2 F ( � * � * � - C$; �B� � FJQ � H<C+L Q K(F?H N+~EwlFJI(B<H H@A!2=( C+wOM1_ ImF?HoA ~EB@2 M

wlF?H _ ImFJwOwlF?H;w ~5Nf~EwlFJI(B0K(F3wzy ~EQWQWBWM'((I(Q.K(C+MOQ �JQWB<F|k :mC+MlHWMlF %j y MOLmK Mlkc~EQWMlC+L K(FxK(RiDz~EI(Q0F?HWQ;k;:mC+MlHWMlFxA ~EB@2 M wlF?H.HWI(MONf~EL Q<F?H:,. ��( �� < �� 2 - I(LmF.Nf~EwlFJI(B�A ~EB�K(RiDz~EI(Q�K(C+L(LmR?F d wzy ~EQWQWBWM'((I(Q�Hcy MOw L y ~EA(A ~EB�~FElQ�A ~+H�Km~ELmH�w ~( ~EwOMlH<F�� - Nf~EwlFJI(B0K(F3wzy ~EQWQWBWM'((I(Q0Q<C+I/�WC+I(B<H�B<F _ I(MlH<F�� - N+~EwlFJI(B0K(F3wzy ~EQWQWBWM'((I(Q0DG~+kJI(wOQ�~EQWMONPF�� .0�1�� - ~EQWQWBWM'((I(Q.K(F3Nf~EwlFJI(B0k?C+LmHWQ�~EL Q<F�K(C+L(LmR?F %

-5%87 c a c FJQ;{fB�~�2L2 ~EMOB<F?H -&-

� qO�!�Rk� "� # �y� j F?HvK(R?kJw ~EB�~EQWMlC+LmHvK y RJwlR32 FJL Q<HxHWI(MONf~EL Q<F?H � HWI(MON+~EL Q.wlF�A(B<C+wlC+{fImF � MOwOwOImH<QWB<FJL Q3wlF?H.K M0/ Rh�B<FJL Q<H;D C+B@2 F?H0K(F+2 C K�0JwlF?H!,

� �&� � ��u/w�~B{(�&| � � � � u/|��*�&}�{`|!v �� !��/x�{��w�u ( ��{��w5u � {F|��!w � � ( ��{!�!w5u �&~&u��!��{(�/| � �(�/w!x�~��&~&u��!��{(�/|.- � � +�{ +5u� � - �� {��w5u ( � � � � � � � - �� {`|��w � ( � � � � � � � - �� {��w5u �&~mu5�!��{(�&| ( � � � � � � � - �� (�&w�x�~��&~mu5�!��{(�&| ( � � � � � � � * +�{ +!w5umz - � �� +�{�+�w5umz �� +�{�+�w5umz w5u&z �� +�{�+5u�� ( � � � � � � � - �� +�{�+5u�� |��F��u ��

n M(k?FJQWQ<F c a c F?HWQ�k?C+L Q<FJL ImF;Km~ELmH I(L \ k :(MlFJB ��5�&x�{!�!w5u ��} �B}5�EI(L K(C kJI�2 FJL Q�Nf~EwOMlK(F�H�FJwlC+Lok?FJQWQ<F c a cF?HWQ:,

� �&� � ��u/w�~B{(�&| � � � � u/|��*�&}�{`|!v � � �� ~J�5�&|!}B��&|5u ��3|'� �� !��/x�{��w�u � � �� 5�&x�{!�!w5u ��} �B}�� 5�/x�{!�!w5u �

� ��{��w�u � � �/| �!��/x�{!��w�u � �(��{��w�u �� {`|��w'� � � u5�!{ou5~�� )�| u(��uF�5x��u }5u } �5��)&��u&|�� 5{`|��w'� �� {��w�u!�&~mu5��{(�&| � �mw5u��Q{��/w5u ~&u��!��{(�/| � �*��{!�!w5u �&~&u��!��{(�/| �� (�&w�x�~ �&~mu5��{(�&| ��'�5{Fw � +�{�+�w5umz w5u&z � � � � � � � � � � � � � � �-� � � x �*)�w x��*)�~o}Bu } *�5��{��B~H�

� �5�*�/w!x�~ �m~&u��!��{*�/| �� {��w�u!�&~mu5��{(�&| � � u5�*�/|B}Bu ~&u5��{*�/| � �(��{!��w�u!�m~&u5��{*�/| �� (�&w�x�~ �&~mu5��{(�&| � � u5�!{ u5~�� )�| �*�/w�x�~o}Bu ~&u��!��{*�/|�� (�&w�x�~��&~mu5�!��{(�&| �� +�{�+5u�o|��F��u � � � � � � �� -� � � �ow mz &w5u/|��/u � � +�{ +�u��

� ��!�5�&x�{��w5u �2

� � � 4)@ � � -$! !�- �� 4�6

j F k �3I(BoK y I(LmF c a c � H^~ELmH wlF?HoK(R?kJw ~EB�~EQWMlC+LmH K y ~EQWQWBWM'((I(Q<H FJQowlF?H5Q�AqA F?H A(B<R?K(Rh\mL(MOLmH � F?HWQ5R _ I(My�Nf~EwlFJL Q<F d I(LmF5{fB�~�2L2 ~EMOB<FoLmC+L5� k?C+L Q<Fh4qQWImFJwOwlF % j F?HvC+A RJB�~EQ<FJI(B<HxK(F=2�I(wOQWMOA(wOMlkJMOQ<R�� F32 A(BWI(L Q<R?H|~EI DGC+B �2 ~EwOMlH@2 F X } fvu �)LmF H<C+L QN_ ImF K I � <��(*K �"$@58 2 $T � � * A C+I(Nf~EL Q��JQWB<F B<F32 A(w ~+k?R?H A ~EB K(F?HoB 0J{fwlF?H K(F{fB�~�2L2 ~EMOB<F?HoHWI(A(A(wlR32 FJL Q�~EMOB<F?H � _ I(M�k;: ~EL({PFJB�~EMOQoI(L A FJI(Q�w ~ D C+B@2 F K(F w ~ H<QWBWImkJQWI(B<F K I K(C kJI�2 FJL Q2 ~EMlH�A ~+H.H�~oHWMO{fL(My\ kc~EQWMlC+L �h%

. ~EB%k?C+L QWB<F��PwlF?H c a c H<C+L Q%K(F?H�{fB�~�2L2 ~EMOB<F?H%K(C+L Q�w ~ \mL ~EwOMOQ<R�L y F?H<Q�A ~+H�Fh4(~+kJQ<F32 FJL Q%w ~ 2��32 F)_ ImFk?FJwOwlF�K(F?H {fB�~�2L2 ~EMOB<F?H�LmC+L5� k?C+L Q<Fh4 QWImFJwOwlF?H)K I�k : ~EA(MOQWB<F%A(B<R?k?R?K(FJL Q % j F?H {fB�~�2L2 ~EMOB<F?H LmC+L5� k?C+L Q<Fh4qQWImFJwOwlF?HH<FJBWNPFJL Q d K(Rh\mL(MOB�K(F?H%HWQWBWImkJQWI(B<F?H�K(F0k;: ~FElLmF?H�DG~EMlH�~EL Q�A ~EBWQWMlFvK y I(L w ~EL({ ~E{PF�DGC+B@2 FJw � LmC+L5� k?C+L Q<Fh4qQWImFJw �h%j F?H0{fB�~�2L2 ~EMOB<F?H.~EI H<FJLmH0K(F?H c a c H<C+L Q;I(QWMOwOMlH�R?F?H;A C+I(B0K(Rh\mL(MOB;w ~5DGC+B@2 F|K y I(LmF|HWQWBWImkJQWI(B<F�K(F|K(C+L5�LmR?F?H�~EB@( C+B<F?H<k?FJL Q<F�� MlkJMmwzy ~EB@( C+B<F?H<k?FJLmk?F.K I k?C+L Q<FJL I K(F;K(CqkJI�2 FJL Q<H � ^ j % <�FJQWQ<F0H<F?k?C+LmK(F0I(QWMOwOMlH�~EQWMlC+LK(F?H {fB�~�2L2 ~EMOB<F?H F?HWQ ~EImH<HWM0QWB 0?H k?C+I(B�~EL Q<F��FJQ C+L ~EA(A FJwOwlF H<C+I(NPFJL Q k?F {PFJL(B<F K(F {fB�~�2L2 ~EMOB<F?H K(F?H �(2$# #�2$T �P*� �� 2 ��% �P*� %

c ~ELmH;wlFxK(C/2 ~EMOLmF|K(F3w ~ k?C/2 A(MOw ~EQWMlC+L FJQ;K(F?H�w ~EL({ ~E{PF?H.K(F3A(B<C+{fB�~�2L2 ~EQWMlC+LM� C+L I(QWMOwOMlH�F3wlF?H�{fB�~�2 �2 ~EMOB<F?H�K y ~EB@((B<F?H A C+I(B|K(Rh\mL(MOB k?FN_ ImF wzy C+L ~EA(A FJwOwlF K(F?H ~EB@((B<F?H K(F H@AqL Q�~F4(F ~�(mHWQWB�~EMOQ<F��kfy F?HWQ � d � K MOB<F

-&6 j Fxw ~EL({ ~E{PF�� ^ j

I(L'~EB@((B<F�_ I(M%B<FJA(B<R?H�FJL Q<F Q<C+I(Q<F w ~ HWQWBWImkJQWI(B<F FJQ5wlF k?C+L Q<FJL I K y I(L A(B<C+{fB�~�2L2 F��2 ~EMlHoKm~ELmH�wlF _ ImFJwQ<C+ImH�wlF?H�~+HWA F?kJQ<H�H@AqL Q�~F4 M1_ ImF?H�Fh4 Q<FJBWLmF?H%K I w ~EL({ ~E{PF�� k?C/2L2 F;wlF0k :mC+My4 K(F?HT2 C+Q<H � kJwlR?H�FJQ�wlF?H%H<MO{fLmF?H%K(FA C+LmkJQWI ~EQWMlC+L � A C+MOL Q<H �zNqMOBW{fI(wlF?H�� NqMOBW{fI(wlF?H�� NPC+MOB<F A ~EB<FJL Q@:�0?H<F?H � H<C+L Q C/2 MlH|kc~EB�K(FJNPFJL ImH MOL I(QWMOwlF?H�I(LmFDGC+MlH)_ ImF3wlF3A(B<C+{fB�~�2L2 F5~ RJQ<R|~EL ~Ew'A H<R|FJQ�B<F?k?C+L(L I k?C+L D C+B@2 F d w ~oH@AqL Q�~F4(F|K I w ~EL({ ~E{PF %p w(F?HWQ)MOL Q<RJB<F?H<H^~EL Q%K(F�LmC+Q<FJB _ ImF�wlF?H A(B<C+A(BWMlRJQ<R?H%K(F?H�{fB�~�2L2 ~EMOB<F?H%LmC+L5� k?C+L Q<Fh4 QWImFJwOwlF?H%H<F�B<FJQWB<C+I(NPFJL Q

Km~ELmH wlFv{fB�~�2L2 ~EMOB<F?H;K y ~EB@((B<F?H % f C+ImH NPFJBWB<C+LmH�K(F?H ~EA(A(wOMlkc~EQWMlC+LmH.K(F3k?FJw ~5~cNPF?k3wlF?H�{fB�~�2L2 ~EMOB<F?H0~EQWQWBWMy�((ImR?F?H3~EI54 k : ~EA(MOQWB<F?H C FJQ �5% <�FJQWQ<F5k?C+BWB<F?HWA C+LmKm~ELmk?F)�[ImHWQWMy\ F|wlF�A(B<C+A CfHvK(F w ~ A(B<R?H<FJL Q<F H<F?kJQWMlC+LM� C$;LmC+ImH;~EwOwlC+LmH 2 ~EMOL Q<FJL ~EL Q0NPC+MOB;k?C/2L2 FJL Q;QWB�~ELmHWA CfH<FJB�I(LmF3{fB�~�2L2 ~EMOB<FxLmC+L5� k?C+L Q<Fh4qQWImFJwOwlF FJL c a c FJQk?C/2L2 FJL Q�R?kJBWMOB<F�I(LmF�A�:(B�~+H<F0K I w ~EL({ ~E{PF;B<F?k?C+L(L I A ~EB�w ~3{fB�~�2L2 ~EMOB<F0H�C+ImH w ~vD C+B@2 F�K y I(L K(C kJI�2 FJL Q� ^ j Nf~EwOMlK(FxA ~EB;B�~EA(A C+BWQ d w ~ c a c A(B<R?k?R?K(FJL Q<F %� QWImK MlFJB;k?FJQWQ<F0QWB�~ELmH<A CfHWMOQWMlC+L A FJI(Q�A ~EB�~FElQWB<FvI(L A(I(B Fh4 FJB<kJMlk?F3K(FvHWQ�AqwlF % c F0DG~EMOQ k?FvL y F?HWQ�A ~+H�Q�~EL Q

w ~vA CfH<HWM'((MOwOMOQ<R K(F QWB�~ELmHWA CfH<FJB I(LmF {fB�~�2L2 ~EMOB<F;FJL I(LmF c a c FJQ�I(LmF A�:(B�~+H<F�Km~ELmH I(L K(CqkJI�2 FJL Q�� ^ j_ I(M)LmC+ImH3MOL Q<RJB<F?H<H<FJB�~H��2 ~EMlH3A(wOI(Q��+Q�wzy R _ I(MONf~EwlFJLmk?F FJL QWB<Fo{fB�~�2L2 ~EMOB<F?H � A�:(B�~+H�F?H�FJQ c a c�� K(C kJI�2 FJL Q_ I(M�N+~ LmC+ImH�A FJB@2 FJQWQWB<F K y I(QWMOwOMlH<FJB|wlF?H�A(B<C+A(BWMlRJQ<R?H�K(F wzy I(LmF Km~ELmH|wlF k?C+L Q<Fh4 Q<F K(F wzy ~EI(QWB<F % f C+ImH�FJLNPFJBWB<C+LmH I(LmF MOwOwOImHWQWB�~EQWMlC+L M'2 A C+BWQ�~EL Q<F ~EI k : ~EA(MOQWB<F � wlC+B<H _ ImF LmC+ImH I(QWMOwOMlH<FJB<C+LmH wlF?H|A(B<C+A(BWMlRJQ<R?HoK(F?H{fB�~�2L2 ~EMOB<F?H|~EQWQWBWM'((ImR?F?H � k;: ~EA(MOQWB<F C� A C+I(Bvk?C/2 A(B<FJLmK B<FowlF?HvM'2 A(wOMlkc~EQWMlC+LmH|H<I(B.w ~ A FJB[DGC+B@2 ~ELmk?FoK(F?HQWB�~ELmH[DGC+B@2 ~EQWMlC+LmH0K(F|K(CqkJI�2 FJL Q<H � ^ j R?kJBWMOQ<F?H0FJL �xn j a %

� I1GU�U� ��F��R��I"�F� �RGU�U� � � �j ~oQWB�~ELmH[DGC+B@2 ~EQWMlC+L K y I(LmF|{fB�~�2L2 ~EMOB<F�LmC+L5� k?C+L Q<Fh4qQWImFJwOwlF5k?C+L D C+B@2 F d k?F*_ ImF3LmC+ImH.~cNPC+LmH0NqI ~EI

k : ~EA(MOQWB<F�A(B<R?k?R?K(FJL Q.NPFJB<H;I(LmF c a c F?HWQ0~+H<H<F��|H<M'2 A(wlF % p w H<IHG Q;K y ~EA(A(wOM1_ ImFJB.wlF?H�B 0J{fwlF?H0HWI(MONf~EL Q<F?H!,$&% j y ~F4qMlC/2 F K(F3w ~o{fB�~�2L2 ~EMOB<F�K(FJNqMlFJL Q;wlF|LmC/2 K I Q�AqA FxK I K(C kJI�2 FJL Q.K(Rh\mL(M A ~EB;w ~ c a c %

�5%). C+I(B k : ~/_ ImF;LmC+L5�zQ<FJB@2 MOL ~Ew K(F;w ~3{fB�~�2L2 ~EMOB<F�� MOL QWB<CqK I(MOB<F0I(L Q�AqA F;K y RJwlR32 FJL Q<H Km~ELmH�w ~ c a c %75%). C+I(B�k;: ~/_ ImF;Q<FJB@2 MOL ~Ew K(F w ~3{fB�~�2L2 ~EMOB<F�� MOL QWB<CqK I(MOB<F;I(L Q�AqA F;K y RJwlR32 FJL Q<H�Q<C+I/�[C+I(B<H�N MlK(F;K(C+L QwlF?H0RJwlR32 FJL Q<H.NPC+L Q;B<FJA(B<R?H<FJL Q<FJB0I(LmF|Cqk?kJI(B<FJLmk?F�K(Fxk?F|Q<FJB@2 MOL ~Ew %

]�%). C+I(B k : ~/_ ImF B 0J{fwlF K(F A(B<C K ImkJQWMlC+LM��I(QWMOwOMlH�FJB5w ~ H<R _ ImFJLmk?F K y RJwlR32 FJL Q<H FJQowzy ~EwOQ<FJBWL ~EQWMONPF A C+I(BQWB�~+K I(MOB<F3w ~ A ~EBWQWMlF3{ ~EImk;:mFxK(F?H B 0J{fwlF?H�K(F.A(B<CqK ImkJQWMlC+L FJL K(Rh\mL(MOQWMlC+L K(FvQ�AqA F3K y RJwlF32 FJL Q<H.Km~ELmHw ~ c a c %

<vy F?HWQ I(L A(B<C k?F?H<H<ImH H@AqH<Q<R32 ~EQWM1_ ImF��T_ I(M A FJI(Q��JQWB<F I(L'A FJI DG~+HWQWMlK MlFJI54 �H2 ~EMlH H�~ELmH �<~�2 ~EMlHoA ~EBk?C+L QWB<F��JQWB<F+((MlFJL k?C/2 A(wOM1_ ImR %

� qO�!�Rk� "� # �1# . Fc~ELmC ~ K(C+L(LmR�I(LmF K(Rh\mL(MOQWMlC+L wlC+{fM1_ ImF=((MlFJL k?C+L(L ImF�A C+I(B.wlF?HvFJL QWMlFJB<HvL ~EQWI(B<FJwlH3FJQwlF?H;C+A RJB�~EQWMlC+LmH;k?C/2L2 Fxwzy ~+K(K MOQWMlC+L % c ~ELmH0k?FJQWQ<FxK(Rh\mL(MOQWMlC+LM�mQ<C+I(Q0FJL QWMlFJB;A FJI(Q��JQWB<FxR?kJBWMOQ.H<C+MOQ;k?C/2L2 FRJQ�~EL Q3w ~ k?C+LmHWQ�~EL Q<F 0 � H<C+MOQ.k?C/2L2 F5wlF5HWImk?k?F?H<H<FJI(B3K y I(L#FJL QWMlFJB n k?F _ I(M)Hcy R?kJBWMOQ s(n)

%QX L Q<FJB@2 F5K(FB 0J{fwlF?H0K(F3{fB�~�2L2 ~EMOB<F�� k?F?kJM A FJI(Q;Hcy R?kJBWMOB<F�,

N → ~ N |�

� Q�~EL Q�K(C+L(LmR K(FJI54 FJL QWMlFJB<H m FJQ n � wzy ~EBWMOQ@:�2 RJQWM1_ ImF K(F . Fc~ELmC K(Rh\mL(MOQxwzy ~+K(K MOQWMlC+L�A ~EB|K(FJI54 B<RJ{fwlF?HK(F B<R?R?kJBWMOQWI(B<F�_ I(M�K MlH�FJL Q�B<F?H<A F?kJQWMONPF32 FJL Q _ ImF wzy ~+K(K MOQWMlC+L K y I(L FJL QWMlFJB5K M0/ RJB<FJL Q K(F 0 � kfy F?H<Q � d � K MOB<FK(F3w ~ DGC+B@2 F s(i) ~cNPF?kxI(LmF|FJL QWMlFJB n A FJI(Q;H<F3B<R?R?kJBWMOB<F|FJL wzy ~+K(K MOQWMlC+L K(F i FJQ s(n) �(FJQ)_ ImF3wzy ~+K(K MOQWMlC+LK(F 0 ~cNPF?k I(L#FJL QWMlFJB n H<F B<R?R?kJBWMOQxFJL n% f C+ImHvB<FJNqMlFJLmK B<C+LmH|~EI k;: ~EA(MOQWB<F C H<I(B.w ~ A(BWMlH<F5FJL k?C/2 A(Q<F

K(F5w ~ B<R?R?kJBWMOQWI(B<F A C+I(BvDz~EMOB<F5wzy ~+K(K MOQWMlC+L %O. C+I(B�wzy MOLmHWQ�~EL Q�� FJL Q<FJB@2 F K(F5{fB�~�2L2 ~EMOB<F�� I(LmF Fh4 A(B<F?H<HWMlC+L

-5%87 c a c FJQ;{fB�~�2L2 ~EMOB<F?H -mC

F?HWQ;H<C+MOQ�wzy ~+K(K MOQWMlC+L K(F|K(FJI54 FJL QWMlFJB<HvH<C+MOQ�I(L FJL QWMlFJB � I(LmF|k?C+LmHWQ�~EL Q<F � ,E → N | �m}�} N N

nqFJwlC+L wlF?H B 0J{fwlF?H R?K MlkJQ<R?F?H kJMy� : ~EI(Q��%wlF LmC+L5�zQ<FJB@2 MOL ~Ew E K(FJN MlFJL Q wlF Q�AqA F K(F K(C kJI�2 FJL Q % c FJI54RJwlF32 FJL Q<H�k?C+BWB<F?HWA C+LmK(FJL Q ~EI545LmC+L5�zQ<FJB@2 MOL ~EI54 E FJQ N

% c ~ELmH%wlF?H�K(FJI54okc~+H��fMOw�Ao~|K(FJI54 ~EwOQ<FJBWL ~EQWMONPF?HK(F.B 0J{fwlF?H�K(F0A(B<CqK ImkJQWMlC+L _ I(M H<F;B<FJQWB<C+I(NPFJL Q0Km~ELmH�wlF?H�K(Rh\mL(MOQWMlC+LmH0K y RJwlR32 FJL Q<H��qA ~EB<FJL Q@:mR?H�R?F?H;k?C/2L2 FMOw�H<F K(C+MOQxA C+I(BxB<F?HWA F?kJQ<FJBxw ~ A(BWMlC+BWMOQ<R K(F?H|C+A RJB�~EQ<FJI(B<H�Km~ELmHxw ~ c a c %�X L5\mLM� QWB<C+MlH|RJwlR32 FJL Q<H|NqMlK(F?HNqMlFJL(LmFJL Q.K(Rh\mL(MOB0wlF?H�QWB<C+MlH�Q<FJB@2 MOL ~EI54 �&}!}5�Q~oFJQ �Bu&w �K,

� �&� � ��u/w�~B{(�&| � � � � u/|��*�&}�{`|!v �� u ( | * (;�&}!} � | � | - - �� | (�(h~ � | - * �5u/w'� - �� &}!} � � � �� ~ �� Bu&w � ��

2

� I1GU�U� k! ��P� ��l�lm��kUMPE�� kH�� "� ��I"�F� �RGH�onH��l�GH�R�B�QM �� CPAPC+LmH 2 ~EMOL Q<FJL ~EL Qxk?C/2L2 FJL Q.A(B<FJLmK B<F I(LmFxA�:(B�~+H<F5~+k?k?FJA(Q<R?F|A ~EB0w ~ {fB�~�2L2 ~EMOB<F�A C+I(B0FJL Dz~EMOB<F

I(L K(CqkJI�2 FJL Q � ^ j Nf~EwOMlK(FxA ~EB;B�~EA(A C+BWQ d w ~ c a c C/((Q<FJL ImF�A ~EB0wlF?H�B 0J{fwlF?H0A(B<R?k?R?K(FJL Q<F?H % j ~ c a cFh4 A(BWM'2 F%w ~�D C+B@2 F�K(F�wzy ~EB@((B<F�K y ~EL ~Ew'AqH�F�k?C+BWB<F?HWA C+LmKm~EL Q d w ~�A�:(B�~+H<F % p wqF?HWQ)~EMOLmH<M A(wOImH DG~+kJMOwlF�K y C/((Q<FJL(MOBwlF K(CqkJI�2 FJL Q � ^ j FJL A ~+H�H�~EL Q K y ~�( C+B<K A ~EB wzy ~EB@((B<F K y ~EL ~Ew'AqH�F K(F w ~#A�:(B�~+H<F % t LmF D C+MlH wzy ~EB@((B<FK y ~EL ~Ew'A H<F B<FJLmK I Fh4 A(wOMlkJMOQ<F�� wlF K(C kJI�2 FJL Q � ^ j A C+I(BWB�~1�JQWB<F C/((Q<FJL ImF FJL DG~EMlH^~EL Q k?C+BWB<F?H<A C+LmK B<F dk : ~/_ ImFvL�3ImK Km~ELmH�k?FJQ�~EB@((B<F.I(L RJwlR32 FJL Q�Km~ELmH�wlFvK(CqkJI�2 FJL Q � ^ j %�� C+MlkJM K(C+Lmk.k?C/2L2 FJL Q�B<Rc~EwOMlH<FJBk?FJQWQ<F|k?C+BWB<F?HWA C+LmKm~ELmk?F&,$&% <�C+LmH<QWBWI(MOB<F|wzy ~EB@((B<F|K y ~EL ~Ew'A H<F|K(F3w ~oA�:(B�~+H�F|FJL I(QWMOwOMlH�~EL Q.w ~5{fB�~�2L2 ~EMOB<F %

�5%�� kJBWMOB<F wlF A(B<C+wlC+{fImF#K I�K(CqkJI�2 FJL Q � ^ j FJL 2 FJQWQ�~EL Q ((MlFJL�k?C/2L2 F c a c k?FJwOwlF _ I(M|~ RJQ<RA(B<Rc~Ew ~�((wlF32 FJL QvK(Rh\mL(MlF�A C+I(B�w ~ {fB�~�2L2 ~EMOB<F�k?C+LmHWMlK(RJB<R?F %

75% a B�~?NPFJB<H<FJB wzy ~EB@((B<F K y ~EL ~Ew'A H<F FJQ A C+I(Bok : ~/_ ImF L�3ImK�B<FJLmk?C+L QWB<R��kJB<R?FJB I(L RJwlR32 FJL Q K I Q A A Fk?C+BWB<F?H<A C+LmKm~EL Qv~EI Q<FJB@2 MOL ~Ew)C+I ~EI LmC+L5�zQ<FJB@2 MOL ~Ew)~EA(A ~EB�~FE H<H^~EL Q.Km~ELmH;wlFxL�3ImK %

]�% j C+B<H _ ImF wlF L�3ImK B<FJLmk?C+L QWB<R Dz~EMOQ ~EA(A ~EB�~FElQWB<F I(L LmC+L5�zQ<FJB@2 MOL ~Ew �%C+L C/((QWMlFJL Q wlF k?C+L Q<FJL I K(Fwzy RJwlR32 FJL Q k?C+BWB<F?HWA C+LmKm~EL Q Km~ELmH5wlF K(CqkJI�2 FJL Q FJL A ~EB<k?C+I(B�~EL Q k : ~+kJI(L'K(F?H L�3ImK(H=\mwlH5FJQoFJLDz~EMlH�~EL Q;w ~ k?C+BWB<F?HWA C+LmKm~ELmk?FxA C+I(B0k : ~+kJI(L K(Fxk?FJI54!� kJM %

� qO�!�Rk� "� # � <�C+LmHWMlK(RJB<C+LmH�w ~xA�:(B�~+H<F add s 0 s s 0 ~+k?k?FJA(Q<R?F;A ~EB�w ~x{fB�~�2L2 ~EMOB<F0K(F�wzy ~EBWMOQ@:�2 RJQWM1_ ImFK(F . Fc~ELmC K(Fxwzy Fh4(F32 A(wlFxA(B<R?k?R?K(FJL Q % j y ~EB@((B<F|K y ~EL ~Ew'A H<F|k?C+BWB<F?H<A C+LmKm~EL Q.F?HWQ:,E

BBBB

yyyy

y

�m}�} N

yyyy

yN

BBBB

~N

~N

BBBB

� ~N

�

-� j Fxw ~EL({ ~E{PF�� ^ j

� I(QWB<F wlF A(B<C+wlC+{fImF K I K(CqkJI�2 FJL Q�� ^ j ��C+L'QWB�~+K I(MOQ w ~ A�:(B�~+H<F FJL'I(L ~EB@((B<F K y RJwlR32 FJL Q<H %>X LA ~EB<k?C+I(B�~EL Q0wzy ~EB@((B<FvK y ~EL ~Ew'A H<F��qwzy RJwlR32 FJL Q�B�~+kJMOLmF.Dz~EMOQ ~EA(A ~EB�~FElQWB<F3wlFvLmC+L5�zQ<FJB@2 MOL ~Ew E ~EI�_ ImFJw C+L Dz~EMOQk?C+BWB<F?HWA C+LmK B<F|I(L RJwlF32 FJL Q.K(F�Q�AqA F u % j F�A(B<F32 MlFJB)\mwlH.K(F|k?F|L�3ImK F?H<Q;wlF|Q<FJB@2 MOL ~EwT�&}�} ~EI�_ ImFJw�C+LDz~EMOQ3k?C+BWB<F?H<A C+LmK B<Fowzy RJwlR32 FJL QxN MlK(F � �m}�}�� % j F?HxK(FJI54#~EI(QWB<F?H \mwlHvD C+L Q|~EA(A ~EB�~FElQWB<F wlF5LmC+L5�zQ<FJB@2 MOL ~EwN ~EI�_ ImFJw d k : ~/_ ImFoD C+MlH3C+L Dz~EMOQxk?C+BWB<F?HWA C+LmK B<F I(L RJwlR32 FJL Q�K(FoQ�AqA F=| %tX L�k?C+L QWMOL I ~EL Q5w ~ k?C+BWB<F?H@�A C+LmKm~ELmk?F�� C+L C/((QWMlFJL Q�wlF0K(CqkJI�2 FJL Q�HWI(MONf~EL Q<C$; C+L B<FJQWB<C+I(NPF�((MlFJL w ~|H<QWBWImkJQWI(B<F.K(F0wzy ~EB@((B<F0K y ~EL ~Ew'A H<FA(B<R?k?R?K(FJL Q ,

� �&� � ��u/w�~B{(�&| � � � � u/|��*�&}�{`|!v �� ~J�5�&|!}B��&|5u � � |'�>� �� u � � �� x5u!�/| � ��}��!}�� u �

� �&}!} � �� | �

� ~�� | � � �Bu&w � � � � �/| �

� �/| �� | �

� ~�� | �

� ~�� | � � �Bu&w � � � � �/| �

� �/| �� /| �

� �!u �

2

� �� 4�686 /�� !�-;6�� 7 �

� <P'�# 3B)WR98S*��

� ��

� ��

� � ��

<�C/2L2 F.A C+I(B�wlF?H%w ~EL({ ~E{PF?H B<RJ{fI(wOMlFJB<H��qMOw F?HWQ%M'2 A C+BWQ�~EL Q�K(FvK MlHWA CfH<FJB�K(F 2 CPAPFJLmH A C+I(B k?C+LmHWQWBWI(MOB<FK(F?H�~+k?k?FJA(Q<FJI(B<H�A C+I(B�wlF�w ~EL({ ~E{PF?H�LmC+L5� k?C+L Q<Fh4 QWImFJwlH�� kc~EB�kfy F?HWQ�FJI54L_ I(M �PK y I(L A C+MOL Q�K(F;NqImF�A(B�~EQWM1_ ImF��A FJB@2 FJQWQ<FJL Q K(F NPRJBWMy\ FJB wzy ~EA(A ~EBWQ<FJL ~ELmk?F�K y I(LmF#k : ~FElLmF � C+I A�:(B�~+H<F � d I(L�k?FJBWQ�~EMOL w ~EL({ ~E{PF LmC+L5�k?C+L Q<Fh4 QWImFJw % <�C/2L2 F�wlF?H%Fh4 A(B<F?H<HWMlC+LmH�B<RJ{fI(wOM10JB<F?H��PwlF?H�{fB�~�2L2 ~EMOB<F?H�LmC+L5� k?C+L Q<Fh4 QWImFJwOwlF?H C / B<FJL Q%I(LN( C+L2 CPAPFJL A C+I(B K(Rh\mL(MOB wlF?H w ~EL({ ~E{PF?H LmC+L5� k?C+L Q<Fh4qQWImFJwlH K(F 2 ~EL(M10JB<F MOL Q<FJLmHWMlC+L(LmFJwOwlF % � A ~EBWQWMOB K y I(LmF{fB�~�2L2 ~EMOB<F��C+L A FJI(Q k :mFJB<k;:mFJB d A(B<C+I(NPFJB K(F?H A(B<C+A(BWMlRJQ<R?H HWI(B wlF w ~EL({ ~E{PF _ I y FJwOwlF K(Rh\mL(MOQ %b^ ~EMlHwzy ~+k?k?FJA(Q<FJI(B�B<F?HWQ<Fvwzy C+I(QWMOw K(F ( ~+H<F.A C+I(B w ~ A(wOI(A ~EBWQ;K(F?H�~EA(A(wOMlkc~EQWMlC+LmH�A(B�~EQWM1_ ImF?H % <�Fvk;: ~EA(MOQWB<FxRJQWImK MlFk?F?H K M0/ RJB<FJL Q<H ~+HWA F?kJQ<H K(F w ~�k?C+LmH<QWImkJQWMlC+L8K(F?H ~+k?k?FJA(Q<FJI(B<H C+I�~EL ~Ew'A H<FJI(B<H A C+I(B wlF?H {fB�~�2L2 ~EMOB<F?HLmC+L5� k?C+L Q<Fh4 QWImFJwOwlF?H %

�:�� = -;: �36 4 # 4�6�:�-;=��0- �;4�6�= � = � / � =.@ 4 %3@ 254�:<6. C+I(Bxk?F,_ I(M�k?C+Lmk?FJBWLmF5wlF?H.{fB�~�2L2 ~EMOB<F?HvLmC+L5� k?C+L Q<Fh4 QWImFJwOwlF?H�� I(L NPCqkc~�((I(w ~EMOB<F ~+Km~EA(Q<R F?HWQ3~EA(A ~EBWI

A C+I(BxA ~EBWwlFJB|K(FoB<F?k?C+L(L ~EMlH<H�~ELmk?F FJQ|K(Fow ~EL({ ~E{PF?H % j�d C$;#A C+I(BxwlF?HxFh4 A(B<F?H<HWMlC+LmH|B<RJ{fI(wOM10JB<F?H|C+L#A ~EBWwlFK(F k : ~FElLmF?HoFJQ K y ~+k?k?FJA(Q<FJI(B<H�� C+L A ~EBWwlF MlkJM�A(wOImH5NPC+wlC+L QWMlFJB<HoK(F A�:(B�~+H�F?H FJQoK y ~EL ~Ew'AqH�FJI(B<H % c ~ELmH wlF?HK(FJI54 kc~+H��mC+L A FJI(Q;A FJLmH<FJB�_ ImF|k?FJw ~oQWMlFJL Q d w ~oA(B<C 4 M'2 MOQ<R ~cNPF?k|wlF|k?C+Lmk?FJA(QvK(Fx{fB�~�2L2 ~EMOB<F�Km~ELmH0wlF?Hw ~EL({ ~E{PF?HvL ~EQWI(B<FJwlH � D B�~EL��c~EMlH�� ~EL({fw ~EMlH�� %'%'% � _ I(M�H<F|B<RiDGRJB<FJL Q d w ~ k?C+LmH<QWBWImkJQWMlC+L K(F?H.A�:(B�~+H<F?H % c ~ELmH.wlFH<F?k?C+LmK kc~+H��qk?FJw ~|QWMlFJL Q�~EImH�HWM A(B<C/( ~�((wlF32 FJL Q0~EI Dz~EMOQ _ ImF.w ~xA(BWMOLmkJMOA ~EwlF|~EA(A(wOMlkc~EQWMlC+L K(F?H�{fB�~�2L2 ~EMOB<F?HLmC+L5� k?C+L Q<Fh4 QWImFJwOwlF?H�F?HWQ�w ~0K(Rh\mL(MOQWMlC+L K(F�w ~0H A L Q�~F4 F�K(F?H�w ~EL({ ~E{PF?H K(F�A(B<C+{fB�~�2L2 ~EQWMlC+L C$; wlF%A(B<C k?F?H�HWImHA ~EB;wlF _ ImFJw�C+L NPRJBWMy\ F�wzy Fh4(~+kJQWMOQWImK(F H@AqL Q�~F4 M1_ ImF|K y I(L A(B<C+{fB�~�2L2 F�F?HWQv~EA(A FJwlR?F�~EL ~Ew'A H<F H@A L Q�~F4qM1_ ImF��K y C$; wlF3Q<FJB@2 F�~EL ~Ew'A H<FJI(B %j y ~EL ~Ew'AqH�F K y I(L w ~EL({ ~E{PF LmC+L5� k?C+L Q<Fh4qQWImFJw0F?H<Q I(LmF A(B<Cqk?R?K I(B<F�_ I(M �)A C+I(B5I(LmF {fB�~�2L2 ~EMOB<F LmC+L5�

k?C+L Q<Fh4 QWImFJwOwlF G = (V, T, P, S) �%NPRJBWMy\ F HWM�I(LmF A�:(B�~+H<F ω ∈ T ∗ ~EA(A ~EBWQWMlFJL Q d L(G) C+I'LmC+L % t L~EwO{PC+BWMOQ@:�2 F HWM'2 A(wlF��)K � d <�Cqk ?PF�� C+I(L({PFJB FJQ �|~+H^~�2 M ��A FJB@2 FJQ K(F Dz~EMOB<F k?FJQWQ<F NPRJBWMy\ kc~EQWMlC+L'A C+I(BL y M'2 A C+BWQ<F _ ImFJwOwlF {fB�~�2L2 ~EMOB<F LmC+L5� k?C+L Q<Fh4qQWImFJwOwlF G

% <�FJQ ~EwO{PC+BWMOQ@:�2 F�F?HWQ ( ~+H<R HWI(B w ~�Q<F?k;:(L(M1_ ImFK(F A(B<C+{fB�~�2L2 ~EQWMlC+L'K5AqL ~�2 M1_ ImF��2 MlFJI54�k?C+L(L ImF FJL�B<F?k;:mFJB<k :mF C+A RJB�~EQWMlC+L(LmFJwOwlF C$;�FJwOwlF A FJB@2 FJQoK(FB<R?H<C+ImK B<F K(F?H A(B<C/((w1032 F?H K(F K(R?kJMlHWMlC+L H<R _ ImFJL QWMlFJwlH % [ N+~EL Q K y ~�( C+B<K(FJB wzy ~EwO{PC+BWMOQ@:�2 F K(Rh\mL(MlH<H�C+LmH w ~DGC+B@2 FxLmC+B@2 ~EwlF|K(F=<>:mC/2 H@?BA ,

O��/�R� �U��/�R�� "� nU� � U��R�� - I(LmF {fB�~�2L2 ~EMOB<F G = (V, T, P, S) F?H<Q K MOQ<F FJLDGC+B@2 F LmC+B@2 ~EwlF K(F�<>:mC/2 H@?!A HWM�FJQ|H<FJI(wlF32 FJL Q HWM�Q<C+I(Q<F?H|wlF?HxA(B<C K ImkJQWMlC+LmH p ∈ P H�C+L QK(F|w ~ D C+B@2 F A → BC C+I A → � C$; A,B,C ∈ V FJQ � ∈ T

%

6&Z <�C+LmHWQWBWImkJQWMlC+L K(F?H0~EL ~Ew'A H<FJI(B<H�A C+I(B;{fB�~�2L2 ~EMOB<F?H;LmC+L5� k?C+L Q<Fh4qQWImFJwOwlF?H

nqC+MOQ I(LmF {fB�~�2L2 ~EMOB<F G = (V, T, P, S) FJQ I(LmF A�:(B�~+H<F x ∈ T ∗ �%K(Rh\mL(MlH<HWMlC+LmH Vijk?C/2L2 F

wzy FJLmH<F32,((wlF�K(F?H LmC+L5�zQ<FJB@2 MOL ~EI54 A ∈ V Q<FJwlH _ ImF A∗⇒ xij

��~EwlC+B<H wzy ~EwO{PC+BWMOQ@:�2 F�HWI(MONf~EL Qkc~EwlkJI(wlFxwlF?H Vij

A C+I(B 1 ≤ i, j ≤ |x| ,$&% k �QG��

i ,87 $ �[ImH _ I y d n� ��I"�F�

�5%Vij = {A | A → � F?H<Q;I(LmF3A(B<C K ImkJQWMlC+L FJQ)_ ImF|wlF i 032 F|H@AB2,( C+wlF|K(F x F?HWQ �&;ST�

75% k �QG��j ,87 � �[ImH _ I y d n

��I"�F�]�% k ��GU�

i ,87 $ � ImH;_ I y d n− j + 1��I"��

-5%Vij

7 ∅65% k ��GU�k ,87 $ �[ImH _ I y d j − 1

� ��IK��CB%

Vij7 Vij ∪ {A | A → BC F?HWQ�I(LmFxA(B<CqK ImkJQWMlC+L FJQ B ∈ Vik

FJQ C ∈ Vi+k,j−k;S��

S��ST�

�� 65%'$ � [ wO{PC+BWMOQ@:�2 F|K(F <�C k;?PF�� C+I(L({PFJB0FJQ �|~+H�~�2 M %

� UE��FrB�R�� J � �9' �>#&* @Q' �>#�2$)+* �6* � 4'�#� �" � >Q' �H8 )W2$@62�6*1@Q'$@ � <P'$@58S* 8 � *>) @ � TA@Q<9) � 2$@58J3H2 ε*� 98 6R9@BR �PR�3H2 � �@B* �(2$# # 2�T �P* *>@ �9' �>#&* @B' ��#�2$)+* �6* � 4'$# �" �j y ~EwO{PC+BWMOQ@:�2 F < � � � A C+I(B <�Cqk ?PF�� C+I(L({PFJB FJQ �|~+H�~�2 M � A(B<FJLmK FJL FJL QWB<R?F I(LmF {fB�~�2L2 ~EMOB<F GFJL�DGC+B@2 F LmC+B@2 ~EwlF K(F�<>:mC/2 H@?BA#FJQ�I(LmF A�:(B�~+H�F x Q<FJwOwlF�_ ImF |x| > 0 � FJQ MOw%K(RJQ<FJB@2 MOLmF A C+I(B|Q<C+I(Q

1 ≤ i, j ≤ |x| FJQ A C+I(B�Q<C+I(Q5LmC+L5�zQ<FJB@2 MOL ~Ew A Hcy MOw�Fh4 MlHWQ<F I(LmF K(RJBWMONf~EQWMlC+L A∗⇒ xij

C$; xijF?H<Q�w ~

H<C+ImH �zA�:(B�~+H�F|K(F x k?C/2L2 FJL��c~EL Q d wzy MOLmK Mlk?F i FJQ0H<F3Q<FJB@2 MOL ~EL Q d wzy MOLmK Mlk?F j%

j y ~EwO{PC+BWMOQ@:�2 F A(B<C k 0?K(F A ~EB MOLmK ImkJQWMlC+L�HWI(B j%b. C+I(B j = 1 � A

∗⇒ xij

H<HWM A → xijF?HWQ I(LmF

A(B<CqK ImkJQWMlC+L K(F w ~ {fB�~�2L2 ~EMOB<F��kc~EB xijK(C+MOQ ~?NPC+MOB A C+I(B|wlC+L({fImFJI(B $&%O. C+I(B j > 1 � A

∗⇒ xij

H<HWM�MOwFh4 MlHWQ<FxI(LmFxA(B<CqK ImkJQWMlC+L ABC FJQ;I(L MOLmK Mlk?F i ≤ k > j Q<FJwlH�_ ImF B K(RJBWMONPF�wlF?H k A(B<F32 MlFJB<HvH@AB2,( C+wlF?HK(F x FJQ C K(RJBWMONPF;wlF?H j−k K(FJBWL(MlFJB<H�H@AB2,( C+wlF?H�K(F x

%m. I(MlH _ ImF k FJQ j−k H<C+L Q%HWQWBWMlkJQ<F32 FJL Q�MOL D RJBWMlFJI(B<Hdj �(MOw�HWIHG Q;K(FxNPRJBWMy\ FJB;wlF?H;K(RJBWMONf~EQWMlC+LmH0FJL C+B<K B<F|kJB<C+MlH<H�~EL Q0K(FxwlC+L({fImFJI(B0K(F|H�C+ImH �zA�:(B�~+H<F?H %j ~ \m{fI(B<F 65%'$ A(B<R?H<FJL Q<Fxwzy ~EwO{PC+BWMOQ@:�2 F < � � % j F3{fB�~ELmK ~cN+~EL Q�~E{PF�K(Fxk?FJQ0~EwO{PC+BWMOQ@:�2 F F?HWQ;H�~5k?C/2 �

A(wlRJQWImK(F A ~EB B�~EA(A C+BWQ d w ~�kJw ~+H<H<F K(F?H w ~EL({ ~E{PF?H LmC+L5� k?C+L Q<Fh4 QWImFJwlH % nqC+L {fB<CfH MOLmk?C+L NPRJL(MlFJL Q F?HWQ H�~k?C+LmH<C/2L2 ~EQWMlC+L K(F�B<F?H<H<C+I(B<k?F?H % c y I(LmF�A ~EBWQ�� FJL A(MOB<F;kc~+H��fC+L A FJI(Q�A(B<FJLmK B<FT�[ImH _ I y d O(n3) RJQ�~EA F?H�K(Fkc~EwlkJI(w A C+I(B0K(R?kJMlK(FJB3HWM x Q<FJwOwlF*_ ImF |x| = n ~EA(A ~EBWQWMlFJL Q d L(G) C+I LmC+L % c y ~EI(QWB<F|A ~EBWQ�� wzy FJLmH<F32,((wlFK(Fvw ~ A�:(B�~+H<F3Km~ELmH�H<C+L FJL QWMlFJB;F?HWQ;~+k?k?R?K(R?F��(K y C$; I(LmFv{fB�~ELmK(Fxk?C+LmH<C/2L2 ~EQWMlC+L K y F?HWA ~+k?FxHWM w ~ A�:(B�~+H<FF?HWQ;K(Fx{fB�~ELmK(F|Q�~EMOwOwlF %

^ �32 F.HWMQ< � �8F?HWQ�Km~ELmH O(n2) A C+I(B�wlF?H�{fB�~�2L2 ~EMOB<F?H%LmC+L5�s~�2=((MO{��mF?H�� FJQ�H<C+I(NPFJL Q%wOMOLmRJB�~EMOB<FvKm~ELmH( Fc~EImk?C+I(A K(F5kc~+H�� MOw L y F?HWQvA ~+H.k?C+LmH<MlK(RJB<R5k?C/2L2 F A(B�~EQWM1_ ImF32 FJL QxI(QWMOwOMlH�~�((wlF % c y ~EI(QWB<F?H3~EwO{PC+BWMOQ@:�2 F?HC+L QvK(C+Lmk|RJQ<RxQWB<C+I(NPR?H _ I(M H�C+L Q)2 C+MOLmH0{PC+I(B@2 ~ELmK(H.FJL Q<F32 AmH.FJQ0FJL F?HWA ~+k?F % j y MOLmk?C+L NPRJL(MlFJL QxK(F|k?F?H~EwO{PC+BWMOQ@:�2 F?H�NqMlFJL Q�K(F k?Fb_ I y MOwlH LmF H<C+L Q�A(wOImH�k?C/2 A(wlFJQ<H�~EI H<FJLmH C$; H<FJI(wlF�I(LmF A ~EBWQWMlF�K(F?H {fB�~�2L2 ~EMOB<F?HLmC+L5� k?C+L Q<Fh4 QWImFJwOwlF?H�A FJI(NPFJL Q �JQWB<F�QWB�~EMOQ<R?F?H%A ~EB%k : ~+kJI(L K(F;k?F?H%~EwO{PC+BWMOQ@:�2 F?H %�^ ~EwO{fB<R�Q<C+I(Q�� k?F?H�kJw ~+H�H<F?HK(Fx{fB�~�2L2 ~EMOB<F?H.Hcy ~?Nm0JB<FJL Q.H<C+I(NPFJL Q.HWIHG H�~EL Q<F?H0FJL A(B�~EQWM1_ ImF %

<�C/2L2 FJL Q H<C+L Q k?C+LmH<QWBWI(MOQ<H k?F?H ~EwO{PC+BWMOQ@:�2 F?H)K y ~EL ~Ew'AqH�F�A(wOImH A FJB[D C+B@2 ~EL Q<H�� X H<H<FJL QWMlFJwOwlF32 FJL Q�H<FJwlC+LK(FJI54 ~F4 F?H % f C+ImH�H�~cNPC+LmH _ ImF A C+I(B�~EL ~Ew'AqH<FJB�I(LmF;A�:(B�~+H<F��fMOwmHWIHG Q%K(F QWB<C+I(NPFJB�I(LmF;K(RJBWMONf~EQWMlC+LM�PC+I K(F2 ~EL(M10JB<FoR _ I(MONf~EwlFJL Q<FoI(L#~EB@((B<FoK y ~EL ~Ew'AqH�F % n M C+L#k?C+LmHWMlK�0JB<F5w ~ K(RJBWMONf~EQWMlC+LM� LmC+ImH|~?NPC+LmH�2 FJL QWMlC+L(LmR~EI k;: ~EA(MOQWB<F ] _ ImFxK(FJI54 {fB�~ELmK(F?H.HWQWB�~EQ<RJ{fMlF?H;H<C+L Q;A CfH<HWM'((wlF?H�A C+I(B�A(B<C K I(MOB<F�I(LmFxK(RJBWMON+~EQWMlC+L ,

65% �L[ L ~Ew'AqH�FxK(F?H<k?FJLmKm~EL Q<F 65$

� � L A FJI(QvA ~EBWQWMOBxK(F wzy ~F4 MlC/2 FoFJQxF?H<H�~ APFJBxK(Fok?C+LmHWQWBWI(MOB<F5w ~ K(RJBWMON+~EQWMlC+L#K(F5{ ~EImk :mF d K B<C+MOQ<F FJLB<F32 A(w ~$�c~EL Q d k;: ~/_ ImF5RJQ�~EA F�I(L LmC+L5�zQ<FJB@2 MOL ~Ew�Km~ELmH0w ~ A(B<C+Q<C+A�:(B�~+H<Fok?C+I(B�~EL Q<F5A ~EB0wzy I(LmF5K(F?HA ~EBWQWMlF|K B<C+MOQ<F|K(F|H�F?H B 0J{fwlF?H0K(F3A(B<CqK ImkJQWMlC+L %

� � L A FJI(Q ~EImH<HWMvA ~EBWQWMOB K(F w ~�A�:(B�~+H<F d K(RJBWMONPFJB FJQ F?H<H�~PAPFJB K(F B<F32 C+L Q<FJB NPFJB<H wzy ~F4qMlC/2 F FJLI(QWMOwOMlH�~EL Q�FJL _ ImFJw1_ ImFvH<C+BWQ<F.K(F?H 2$@Q8UT ��6R �>T �F2 8UTU'$@� vC$; C+L B<F32 A(w ~+k?FvI(LmFvH<R _ ImFJLmk?FvK(FvH@AB2,( C+wlF?HQ<FJB@2 MOL ~EI54 C+I LmC+L5�zQ<FJB@2 MOL ~EI54 Km~ELmH w ~#A(B<C+Q<C+A�:(B�~+H<F k?C+I(B�~EL Q<F A ~EB I(L LmC+L5�zQ<FJB@2 MOL ~Ew.A C+I(BC/((Q<FJL(MOB;w ~oA(B<C+Q<C+A�:(B�~+H<F|A(B<R?k?R?K(FJL Q<F %c ~ELmH wlF kc~+H K(F w ~ k?C+LmHWQWBWImkJQWMlC+L8K(F { ~EImk :mF d K B<C+MOQ<F��k?FJw ~ B<FJNqMlFJL Q d k?C+LmHWQWBWI(MOB<F wzy ~EB@((B<F#K(F

K(RJBWMONf~EQWMlC+LoK(F%w ~;B�~+kJMOLmF�NPFJB<H�wlF?H DGFJI(MOwOwlF?H��Ekfy F?HWQ � d � K MOB<F K(F�K I : ~EI(Q)NPFJB<H wlF>( ~+H��EK y C$; wlF%LmC/2 K y+2�@Q2$) "F �*�6*� <7*>@��62$@58S* % c ~ELmH�wlF.H�F?k?C+LmK kc~+H�� MOw Hcy ~E{fMOQ A(wOI(Q��+Q�K(F.k?C+LmHWQWI(MOB<Fvwzy ~EB@((B<F3K(F?H�D FJI(MOwOwlF?H�NPFJB<H w ~�B�~+kJMOLmF��K y C$; wlFvLmC/2 K y+2�@Q2$) "F �*!2$ 9<7*>@�� 2$@58S* % f C+ImH�~EwOwlC+LmH NPC+MOB A(wOImH A(B<R?kJMlH<R32 FJL Q0k?F?H K(FJI54 ~EA(A(B<C k;:mF?H;Km~ELmHwlF?H�A(B<Cqk : ~EMOLmF?HvH<F?kJQWMlC+LmH %

�:�� = -;: �36 4 # 4�6 /�4�= #5-;=.@ 4

<�C/2L2 F H<C+L LmC/2�wzy MOLmK M1_ ImF�� wzy ~EL ~Ew'A H<F K(F?H<k?FJLmKm~EL Q<F k?C+LmH<MlHWQ<F d k?C+LmH<QWBWI(MOB<Fow ~ K(RJBWMON+~EQWMlC+L�K(F5w ~A�:(B�~+H<F.FJL A ~EBWQ�~EL Q K(F;wzy ~F4 MlC/2 F0FJQ�FJL ~EwOw ~EL Q�NPFJB<H�w ~|A�:(B�~+H<F %�X wOwlF.Hcy ~EA(A(wOM1_ ImF d K(F?H%{fB�~�2L2 ~EMOB<F?H _ I(MLmF%H�C+L Q)A ~+H B<R?kJI(B<HWMONPF?H d { ~EImk;:mF % <�C+LmHWMlK(RJB<C+LmH�K y ~�( C+B<K wzy MlK(R?F%{PRJLmRJB�~EwlF�K(F�wzy ~EA(A(B<Cqk :mF K(F?H<k?FJLmKm~EL Q<F��~?Nf~EL QvK y FJL NPC+MOB;wlF?H;K M0/ RJB<FJL Q<F?H.N+~EBWM ~EL Q<F?H %

�� '� � �� '� �� &� � � �

j y MlK(R?Fx{PRJLmRJB�~EwlFxK(Fxk?FJQWQ<F|~EA(A(B<Cqk :mF|k?C+LmHWMlH<Q<F d A ~EBWQWMOB;K(F3wzy ~F4 MlC/2 F d k?C+LmHWMlK(RJB<FJB�w ~5A�:(B�~+H<F3A C+I(BH<F3K(F32 ~ELmK(FJB0k?C/2L2 FJL Q.K(RJBWMONPFJB�wlF?H�A(B<F32 MlFJB<H;H A!2=( C+wlF?H;K(F3w ~ A�:(B�~+H<FxFJL B<F32 A(w ~$�c~EL Q0wzy ~F4 MlC/2 F3A ~EBwzy I(LmF|K(F?H�A ~EBWQWMlF?H.K B<C+MOQ<F?H0K(FxH<F?H;B 0J{fwlF?H0K(F3A(B<CqK ImkJQWMlC+L %t LmF�DGC+MlH�w ~3A(B<F32 M10JB<F;K(RJBWMONf~EQWMlC+L Dz~EMOQ<F��fK(F;K(FJI54 k :mCfH�F?H�wzy I(LmF:,PH<C+MOQ�C+L ~vMOL QWB<CqK I(MOQ%I(LmF�H<R _ ImFJLmk?F

K(F3Q<FJB@2 MOL ~EI54 ~EI K(R3((I(Q;K(F.w ~5LmC+I(NPFJwOwlF3A(B<C+Q<C+A�:(B�~+H�F|k?C+I(B�~EL Q<F��mH�C+MOQ�w ~�LmC+I(NPFJwOwlF|A(B<C+Q<C+A�:(B�~+H<Fxk?C+I5�B�~EL Q<F#k?C/2L2 FJLmk?F A ~EB I(L LmC+L5�zQ<FJB@2 MOL ~Ew % n M3K(F?H LmC+L5�zQ<FJB@2 MOL ~EI54 H<C+L Q ~EA(A ~EBWImH ~EI K(R3((I(Q K(F w ~A(B<C+Q<C+A�:(B�~+H<F k?C+I(B�~EL Q<F�� C+L#wlF?H|~EA(A ~EBWMlF ~cNPF?k wlF?H3Q<FJB@2 MOL ~EI54�K(R3((I(Q�~EL Q w ~ A�:(B�~+H�F FJQxk?F � ImH _ I y d k?F_ I y C+L B<FJLmk?C+L QWB<F I(L LmC+L5�zQ<FJB@2 MOL ~Ew;Km~ELmHow ~ A(B<C+Q<C+A�:(B�~+H<F k?C+I(B�~EL Q<F % j C+B<H _ I y I(L'LmC+L5�zQ<FJB@2 MOL ~Ew;F?HWQ~EQWQ<FJMOL Q Km~ELmH w ~ A(B<C+Q<C+A�:(B�~+H�F k?C+I(B�~EL Q<F��C+L H<F K(F32 ~ELmK(F d LmC+I(NPFc~EI k?C/2L2 FJL Q {PRJLmRJB<FJB wlF?H A(B<C��k : ~EMOLmH�Q<FJB@2 MOL ~EI54�Km~ELmH3w ~ A�:(B�~+H<F FJL#wlF5B<F32 A(w ~$�c~EL Q5A ~EBxwzy I(LmF K(F?HxA ~EBWQWMlF?H|K B<C+MOQ<F?H|K(F H�F?HxB 0J{fwlF?HK(F A(B<C K ImkJQWMlC+L %tX Qx~EMOLmHWM�K(F5HWI(MOQ<F�� ImH;_ I y d k?F=_ ImF|w ~ A�:(B�~+H<Fo~EMOQ.A(I �JQWB<F�A(B<CqK I(MOQ<F�� C+Ip�[ImH _ I y d k?F_ ImF0wzy C+L B<FJLmk?C+L QWB<F3I(L H@AB2,( C+wlF0Q<FJB@2 MOL ~Ew Km~ELmH�w ~ A(B<C+Q<C+A�:(B�~+H<F3k?C+I(B�~EL Q _ I(M LmFvHcy ~EA(A ~EBWMlFvA ~+H ~cNPF?kwlF3A(B<Cqk : ~EMOL Q<FJB@2 MOL ~Ew)Km~ELmH�w ~oA�:(B�~+H<F %n M C+L ~EBWBWMONPF d I(L R?k :mF?k HWI(B;wzy ~EA(A ~EBWMlF32 FJL QxK I A(B<Cqk : ~EMOL Q<FJB@2 MOL ~Ew�Km~ELmH0w ~ A�:(B�~+H<F d A ~EBWQWMOB.K I

A(B<Cqk : ~EMOL Q<FJB@2 MOL ~Ew�Km~ELmH w ~ A(B<C+Q<C+A�:(B�~+H<F��)~EwlC+B<HoK(F K(FJI54 k :mCfH<F?H wzy I(LmF , H<C+MOQ5MOw�Dz~EI(Q�B<F32 FJQWQWB<F FJLkc~EImH<Fxwzy I(L K(F?H0k;:mC+My4 K(FxB 0J{fwlF�K(FxA(B<CqK ImkJQWMlC+L DG~EMOQ<H;K(FJA(I(MlH.wlF|K(R3((I(QvK(Fxwzy ~EL ~Ew'AqH�F|A C+I(B0F?H<H�~PAPFJB.K(FK(RJBWMONPFJB;~EI(QWB<F32 FJL Q w ~�A�:(B�~+H<F�� H�C+MOQ�MOw L y A ~|A ~+H�K y ~EI(QWB<F?H k :mC+My4 A CfH<H<M'((wlF?H � FJQ C+L FJL F?HWQ H��(B � ~EI�_ ImFJwkc~+H��(C+L A FJI(Q;K(R?kJw ~EB<FJB _ ImF3w ~oA�:(B�~+H<F3L y ~EA(A ~EBWQWMlFJL Q.A ~+H.~EI w ~EL({ ~E{PF|K(Rh\mL(M A ~EB;w ~ {fB�~�2L2 ~EMOB<F %j F�A(B<Cqk?F?H<HWImH�_ ImF|LmC+ImHvNPFJLmC+LmH3K(R?kJBWMOB<Fok?C+BWB<F?HWA C+LmK FJL DG~EMOQ d I(LmF�DGC+I(MOwOwlF Km~ELmHvI(L#~EB@((B<F A C+I(B

QWB<C+I(NPFJB|w ~ K(RJBWMONf~EQWMlC+L d { ~EImk :mF K(Fow ~ A�:(B�~+H�F d ~EL ~Ew'AqH<FJB % t L L�3ImK�Km~ELmH|k?FJQWQ<F ~EB@((B<F K(F5DGC+I(MOwOwlFk?C+BWB<F?HWA C+LmK d I(LmF A(B<C+Q<C+A�:(B�~+H<F { ~EImk :mF ~EwlC+B<H _ I y I(L ~EB<k k?C+BWB<F?HWA C+LmK d I(LmF K(RJBWMONf~EQWMlC+L d { ~EImk;:mFA ~EB;wzy I(LmF|K(F?H;B 0J{fwlF?H0K(F3A(B<CqK ImkJQWMlC+L %

6 � <�C+LmHWQWBWImkJQWMlC+L K(F?H0~EL ~Ew'A H<FJI(B<H�A C+I(B;{fB�~�2L2 ~EMOB<F?H;LmC+L5� k?C+L Q<Fh4qQWImFJwOwlF?H

� qO�!�Rk� "�� " nqC+MOQ;w ~5{fB�~�2L2 ~EMOB<F&,S → � A }A → � + | �

. C+I(B.k?FJQWQ<Fx{fB�~�2L2 ~EMOB<F�QWB 0?H;HWM'2 A(wlF��(wzy ~EB@((B<F|K(FxD C+I(MOwOwlFxF?HWQ)\mL(M � MOw�~5w ~5DGC+B@2 FxHWI(MON+~EL Q<F�,

S�� A }

u} ssssss (

JJJ

JJJ

�&� +B} �&�&}. C+I(BWQ�~EL Q��EwlC+B<H _ I y C+LxD C+I(MOwOwlF�k?FJQ)~EB@((B<F�A C+I(B)~EL ~Ew'A H<FJB w ~;A�:(B�~+H<F �&�&}5�cw ~�A(B<F32 M10JB<F%K(RJBWMONf~EQWMlC+L F?H<QO((MlFJLS ⇒ � A }Q��2 ~EMlH�w ~ H<I(MON+~EL Q<F|A CfH<FxK(F?H0K M0G kJI(wOQ<R?H % j F|H@AB2,( C+wlF yy�qy MOL QWB<CqK I(MOQvFJL A(B<F32 M10JB<F�A CfH<MOQWMlC+Lk?C+BWB<F?HWA C+LmK ((MlFJL ~EI A(B<F32 MlFJBxH@A!2=( C+wlFoK(F w ~ A�:(B�~+H�F d B<F?k?C+L(L ~FElQWB<F��t2 ~EMlHvwlF H<F?k?C+LmK H@AB2,( C+wlF�� y �(yW�~EA(A ~EB�~FElQ d w ~ DGC+MlH|Km~ELmH�w ~�((B�~ELmk :mF K(F { ~EImk :mF FJQ�Km~ELmH|w ~ ((B�~ELmk :mF K(F K B<C+MOQ<F K I#L�3ImK�k?C+I(B�~EL QK(F3wzy ~�((B<F|K(FvDGC+I(MOwOwlF %�X L k?C+LmHWMlK(RJB�~EL Q.K y ~�( C+B<K wlF3L�3ImK K(Fx{ ~EImk;:mF��mC+L B<F?k?C+L(L ~FElQ�((MlFJL wlF y �myW�52 ~EMlHwlC+B<H _ I y C+L A ~+H<H<Fo~EI H A!2=( C+wlFoHWI(MONf~EL Q y } y Km~ELmH3w ~ A�:(B�~+H<F d ~EL ~Ew'A H<FJB�� C+L#R?k :mC+ImF d B<F?k?C+L(L ~FElQWB<F wlFy + y MOL QWB<CqK I(MOQ;Km~ELmH�w ~|A(B<C+Q<C+A�:(B�~+H�Fxk?C+I(B�~EL Q<F % psw Dz~EI(Q�K(C+LmkvB<FJNPFJL(MOB d w ~�A(B<C+Q<C+A�:(B�~+H�F.A(B<R?k?R?K(FJL Q<F|FJQQ<FJL Q<FJB�w ~5K(FJI54 M1032 FxK(RJBWMON+~EQWMlC+L A CfH<HWM'((wlF��B_ I(M K(C+L(LmF3w ~ A(B<C+Q<C+A�:(B�~+H<F �&�&}L_ I(M k?C+BWB<F?HWA C+LmK ((MlFJL d w ~A�:(B�~+H<F d ~EL ~Ew'A H<FJB %

2

� qO�!�Rk� "�� 1D j ~o{fB�~�2L2 ~EMOB<F HWI(MON+~EL Q<F|FJL({PFJLmK B<FxwlFxw ~EL({ ~E{PF L = {ω � ωR |ω ∈ ( � | + )∗} ,S → � | � S � | + S +

j y B@((B<F|K(FxD C+I(MOwOwlF|FJL({PFJLmK B<R d A ~EBWQWMOB0K(Fxk?FJQWQ<Fx{fB�~�2L2 ~EMOB<F F?HWQ!,

S

nv dddddddddddddddddddddddddddd

dddddddddddddddddddddddddddd

v~ uuuu

uuu

uuu

'/XXXXXXXXXXXXXXXXXXX

XXXXXXXXXXXXXXXXXXX

� � S �nv ddddddddddddddddddddddddddd

ddddddddddddddddddddddddddd

ow fffffffffffffffff

fffffffffffffffff

��

+ S +

px iiiiiiiiiiiii

iiiiiiiiiiiii

u} rrrrrrrrrr

%-RRRRRRR

RRRRRRR

�5�/� �� S �!�u} rrrr

rrr

rrrrrrr

�� 'HH

HHHH

HHHH

HH��+ S +5�

t| pppppppppp

�� (IIIIII

IIIIII+��+ +5� S � +u} rr

rrrrr

rrrrrrr

�� "*LLLLLLL

LLLLLLL+�+ S + +

w� vvvv

vv

vvvv

vv

�� 'HH

HHHH

HHHH

HH%'%'% %'%'% %'%'% ��+��+5� %'%'% %'%'% %'%'% %'%'% %'%'% %'%'% %'%'% %'%'%

n MmC+L NPFJI(Q�B<F?k?C+L(L ~FElQWB<F0w ~vA�:(B�~+H<F � +�� +�� fC+L K(C+MOQ%K y ~�( C+B<K k :mC+MlH<MOB�w ~3K(RJBWMON+~EQWMlC+L S ⇒ � S ��+A(I(MlH _ ImFkfy F?HWQ3w ~ H<FJI(w d k?FJQWQ<FoRJQ�~EA F _ I(M)A FJB@2 FJQxK y MOL QWB<C K I(MOB<F I(L#H@AB2,( C+wlF y �(y FJL A(B<F32 M10JB<FoA CfHWMOQWMlC+L#K(F5w ~A(B<C+Q<C+A�:(B�~+H<F k?C+I(B�~EL Q<F % <�F H@AB2,( C+wlF B<F?k?C+L(L IM�)wlF A(B<Cqk : ~EMOL'H@AB2,( C+wlF d B<F?k?C+L(L ~FElQWB<F RJQ�~EL Q y + yW�)C+Lk :mC+MlH<MOQ�w ~ K(RJBWMONf~EQWMlC+L � S � ⇒ � + S +5� %BX L5\mLM�m~EA(B 0?H w ~�B<F?k?C+L(L ~EMlH�H�~ELmk?FxK I#y + yW�qwlFvA(B<C k;: ~EMOL H@AB2,( C+wlFd B<F?k?C+L(L ~FElQWB<F�RJQ�~EL Q yy�qyW�(C+L k :mC+MlHWMOQ0w ~ K(RJBWMON+~EQWMlC+L HWI(MON+~EL Q<F|k?C/2L2 F ��+ S +�� ⇒ ��+�� +�� %

2

c F k?FJQWQ<F Fh4 A(wOMlkc~EQWMlC+L {PRJLmRJB�~EwlF FJQoK(F?H5Fh4 F32 A(wlF?H A(B<R?k?R?K(FJL Q<H�� C+L k?C+L5\mB@2 F�_ ImF wzy ~EL ~Ew'A H<F K(F?H �k?FJLmKm~EL Q<F�A(B<C K I(MOQ.FJL DG~EMOQ�I(LmF|K(RJBWMONf~EQWMlC+L d { ~EImk;:mF�� Km~ELmH�w ~ 2 F?H<I(B<FxC$; FJL ~?Nf~EL��c~EL QvFJL A ~EB�~EwOw10JwlFKm~ELmH�w ~ A(B<C+Q<C+A�:(B�~+H<F|k?C+I(B�~EL Q<F|FJQ;Km~ELmH�w ~ A�:(B�~+H<F d ~EL ~Ew'A H<FJB�� C+L B<R?K I(MOQ�Q<C+I/�[C+I(B<H;wlF3LmC+L5�zQ<FJB@2 MOL ~EwwlF;A(wOImH d { ~EImk;:mF.Km~ELmH�w ~xA(B<C+Q<C+A�:(B�~+H�F % <�FJQWQ<F.kc~EB�~+kJQ<RJBWMlHWQWM1_ ImFvF?H<Q%k?C/2L2�I(LmF d Q<C+I(Q<F?H�wlF?H�N+~EBWM ~EL Q<F?HK(Fxwzy ~EL ~Ew'A H<FxK(F?H<k?FJLmKm~EL Q<F %

. ~EB@2 M wlF?H�N+~EBWM ~EL Q<F?H�K(F0wzy ~EL ~Ew'A H<F3K(F?H<k?FJLmKm~EL Q<F�� wzy ~EL ~Ew'AqH<F.LmC+L5�zA(B<R?K MlkJQWMONPF3Nf~|B<F32 FJQWQWB<F3FJL kc~EImH<FwlF?H k :mC+My4 K(F?H B 0J{fwlF?H DG~EMOQ<H K(FJA(I(MlH wlF K(R3((I(Q K(F wzy ~EL ~Ew'AqH<F FJL�kc~+H K y R?k :mF?k#K(F wzy ~EA(A ~EBWMlF32 FJL Q K IA(B<Cqk : ~EMOL'Q<FJB@2 MOL ~Ew d B<F?k?C+L(L ~FElQWB<F��A ~EB Fh4(F32 A(wlF FJL I(QWMOwOMlH�~EL Q wlF B<FJQ<C+I(B ~EBWBWM10JB<F��FJQ k?F Q�~EL QN_ I y MOwFh4 MlHWQ<FxK y ~EI(QWB<F?H0k;:mC+My4 A CfH<HWM'((wlF?H % <vy F?HWQ;wlFxkc~+H;K(Fxwzy Fh4(F32 A(wlF 65%'$&%

65% �L[ L ~Ew'AqH�FxK(F?H<k?FJLmKm~EL Q<F 6&7

c ~ELmH.wzy ~EL ~Ew'A H<F�A(B<R?K MlkJQWMONPF�� C+L N+~ Hcy MOL Q<RJB<F?H<H�FJB d I(LmF kJw ~+H<H�F�K(F|{fB�~�2L2 ~EMOB<F?HvLmC+L5� k?C+L Q<Fh4qQWImFJwOwlF?HA C+I(B�wlF?H _ ImFJwOwlF?H MOw F?HWQ�A CfH<HWM'((wlF3K(F3K(R?kJMlK(FJB d k?C+I(A H��(B d k : ~/_ ImFxRJQ�~EA F+_ ImFJwOwlF3B 0J{fwlFxK(F3A(B<CqK ImkJQWMlC+Lk :mC+MlH<MOB3FJL B<FJ{ ~EB<Km~EL Q|H<M'2 A(wlF32 FJL QxwlF?H�_ ImFJw1_ ImF?HvA(B<C k;: ~EMOLmH3Q<FJB@2 MOL ~EI54 d A(B<C K I(MOB<FoKm~ELmHvw ~ A�:(B�~+H<Fd ~EL ~Ew'AqH�FJB % <vy F?HWQ wlF kc~+H K(F wzy Fh4 F32 A(wlF 65% �5% <�FJQWQ<F kJw ~+H<H�F K(F {fB�~�2L2 ~EMOB<F F?HWQ ~EA(A FJwlR?F LL(k) ��k?F_ I(M�NPFJI(Q3K MOB<F=_ I y FJwOwlF5F?HWQv~EL ~Ew'A H�~�((wlFoFJL A ~EB<k?C+I(B�~EL Q3w ~ A�:(B�~+H<F d B<F?k?C+L(L ~FElQWB<F5K(F { ~EImk :mF d K B<C+MOQ<F� � )+* �>8 8 ' ��T 4 8 9<P2�@�@�TA@ '��:8A4H*!T @�3��8 � � A ~EB0K(RJBWMONf~EQWMlC+L d { ~EImk;:mF � � )+* �98U#�' >8 �6* �>T �F2 8UTU'$@�� ~cNPF?k kH@AB2,( C+wlF?H3K(F�A(B<RJNqMlHWMlC+L % j F?H k H@AB2,( C+wlF?H3K(F�A(B<RJNqMlHWMlC+L Hcy MOL Q<FJBWA(B 0JQ<FJL Q�k?C/2L2 F5wlF|Dz~EMOQ _ I y d k : ~/_ ImFRJQ�~EA F K(FoK(RJBWMONf~EQWMlC+L C+L A FJI(Qvk;:mC+MlHWMOB d k?C+I(A H��(Bvw ~ A(B<C k;: ~EMOLmF B 0J{fwlFoK(F A(B<C K ImkJQWMlC+L d I(QWMOwOMlH<FJBxC+IK(R?K I(MOB<F�wzy R?k :mF?k�K(F�w ~;K(RJBWMONf~EQWMlC+LoFJL�B<FJ{ ~EB<Km~EL Q HWM'2 A(wlF32 FJL Q)wlF?H k A(B<Cqk : ~EMOLmH H@AB2,( C+wlF?H d B<F?k?C+L(L ~FElQWB<FKm~ELmH�w ~oA�:(B�~+H�F %�X L A(B�~EQWM1_ ImF��mC+L H<F3wOM'2 MOQ<F�wlF3A(wOImH;H<C+I(NPFJL Q d K(F?H�{fB�~�2L2 ~EMOB<F?H LL(1)

%

��

j ~�K(F?H�k?FJL Q<F.B<R?kJI(B<HWMONPF.F?H<Q%I(LmF.Q<F?k :(L(M1_ ImF0{PRJLmRJB�~EwlF3K(F0k?C+LmH<QWBWImkJQWMlC+L K y ~EL ~Ew'A H<FJI(B<H�K(F?H<k?FJLmKm~EL Q<H %X wOwlF A FJI(Q H<F�Dz~EMOB<F ~cNPF?k C+I H�~ELmH B<FJQ<C+I(B�~EBWBWM10JB<F��xkfy F?HWQ � d � K MOB<F FJL ~EL ~Ew'AqH�F�A(B<R?K MlkJQWMONPF'C+I LmC+L5�A(B<R?K MlkJQWMONPF % j y MlK(R?F {PRJLmRJB�~EwlF K(F k?C+LmH<QWBWImkJQWMlC+L K y I(L ~EL ~Ew'A H<FJI(BoA ~EB5K(F?H�k?FJL Q<F B<R?kJI(B<HWMONPF k?C+LmHWMlHWQ<F dR?kJBWMOB<F3I(LmFvA(B<C k?R?K I(B<F3A C+I(B�k : ~+kJI(L K(F?H�H@AB2,( C+wlF?H�LmC+L5�zQ<FJB@2 MOL ~EI54 K(F.w ~ {fB�~�2L2 ~EMOB<F % <�FJQWQ<FvA(B<Cqk?Rh�K I(B<F|F?HWQ;k;: ~EBW{PR?F�K y ~EA(A(wOM1_ ImFJB0wlF?H;K M0/ RJB<FJL Q<F?H0B 0J{fwlF?H0K(F3A(B<CqK ImkJQWMlC+L A C+I(B0~EL ~Ew'AqH�FJB;w ~5A�:(B�~+H<F %

[ A(A(wOM1_ ImFJBxI(LmFoB 0J{fwlF K(FoA(B<C K ImkJQWMlC+L F?HWQ3B<FJw ~EQWMONPF32 FJL Q H<M'2 A(wlF % � L�k?C+LmHWMlK�0JB<F wlF?HxH@AB2,( C+wlF?H|K(Fw ~ A ~EBWQWMlF�K B<C+MOQ<F Km~ELmH wzy C+B<K B<F�K(F 2 ~EL(M10JB<F d k?F�_ ImF wzy ~EA(A(wOMlkc~EQWMlC+L K y I(LmF#B 0J{fwlF�K(F#A(B<CqK ImkJQWMlC+LHcy MOL Q<FJBWA(B 0JQ<F k?C/2L2 F�w ~ �Ek?C+LmH<C/2L2 ~EQWMlC+L�� Km~ELmH;w ~oA�:(B�~+H�F�K(FxQ<C+ImH0wlF?H;Q<FJB@2 MOL ~EI54 K(RJBWMONPR?H d A ~EBWQWMOBK(Fok?FJQWQ<F5B 0J{fwlF %�. C+I(B|k;: ~/_ ImF H@AB2,( C+wlF5Q<FJB@2 MOL ~Ew>� � C+L MOLmH 0JB<FoKm~ELmH3w ~ A(B<Cqk?R?K I(B<FoI(L�~EA(A FJw d I(LmFA(B<Cqk?R?K I(B<FN} ��/��!u/w _ I(M�Nf~ k :mFJB<k;:mFJB d ~EA(A ~EBWMlFJB wlF H@AB2,( C+wlF�� Km~ELmH�w ~ A�:(B�~+H<F FJQ�HWM�k?FJw ~ B<RJImH<HWMOQNf~ A ~+H<H<FJB ~EI H@AB2,( C+wlF HWI(MONf~EL Q Km~ELmH w ~ A�:(B�~+H<F � C+L K MOQN_ I y C+L �6R(<P2�)W* k?F H@AB2,( C+wlF��C+Io_ I y C+L wlFk?C+LmH<C/2L2 F �h%/. C+I(B k;: ~/_ ImF H@AB2,( C+wlF�LmC+L5�zQ<FJB@2 MOL ~Ew A �EC+L MOLmH 0JB<F�I(L ~EA(A FJw d w ~0A(B<Cqk?R?K I(B<F�k?C+LmH<QWBWI(MOQ<FA C+I(B;A C+I(B.k?F�H@AB2,( C+wlF*_ I(M �(A ~EB.K(Rh\mL(MOQWMlC+LM� N+~ok?C+LmH�C/2L2 FJB.Q<C+ImH0wlF?H;Q<FJB@2 MOL ~EI54 FJL({PFJLmK B<R?H.A ~EB.k?FLmC+L5�zQ<FJB@2 MOL ~Ew�Km~ELmH0w ~5A�:(B�~+H<F � d A ~EBWQWMOB.K(F3w ~oA CfH<MOQWMlC+L k?C+I(B�~EL Q<F �h%� L#w ~ELmk?Fowzy ~EL ~Ew'AqH<F FJL�~EA(A FJw ~EL Q|w ~ A(B<Cqk?R?K I(B<F k?C+BWB<F?HWA C+LmKm~EL Q<F d wzy ~F4 MlC/2 F % � L A ~EBWwlF K(F K(F?H �

k?FJL Q<F5A ~EB<k?F _ I y MOw)Hcy ~E{fMOQ3K y I(LmF5~EL ~Ew'A H<F�K(F?H�k?FJLmKm~EL Q<F % � L K MOQvB<R?kJI(B<HWMONPF A ~EB<k?F=_ ImF|wlF?H.A(B<Cqk?R?K I(B<F?HHcy ~EA(A FJwOwlFJL Q|wzy I(LmFowzy ~EI(QWB<F�� FJQvwlC+B<H;_ I y MOwTA ~ B<R?kJI(B<H<MON MOQ<R Km~ELmH3wlF?H|B 0J{fwlF?HxK(FoA(B<C K ImkJQWMlC+L � k?FL_ I(M�F?HWQA(B<F?H _ ImF3Q<C+I/�[C+I(B<H0wlFxkc~+H � �mk?FJQWQ<FxB<R?kJI(B<H<MON MOQ<R|H�F3B<FJQWB<C+I(NPF|Km~ELmH;wlF?H0~EA(A FJwlH;K(Fxwzy ~EL ~Ew'A H<FJI(B %

� ��`lm�!�QMP� �FE!l�GU�F�`I �Q� ��Q��;kH��E�n�IKlmM`I �Q�c ~ELmHvI(L#~EL ~Ew'AqH�FJI(B.A ~EB3K(F?H<k?FJL Q<F5B<R?kJI(B<HWMONPF5LmC+L5�zA(B<R?K MlkJQWMONPF�� k?C/2L2 F5LmC+ImHvwzy ~?NPC+LmH�2 FJL QWMlC+L(LmR��

MOw�Dz~EI(Q��JQWB<F FJLo2 F?HWI(B<F K(F B<FJNPFJL(MOB FJL ~EBWBWM10JB<F HWI(B w ~ Q<FJL Q�~EQWMONPF K(F K(RJBWMONf~EQWMlC+L FJL B<F32 FJQWQ�~EL Q FJLkc~EImH<F wlF?H k;:mC+My4 K(F B 0J{fwlF?H|Dz~EMOQ<H�A(B<R?k?R?K(F32L2 FJL Q % t L ~EwO{PC+BWMOQ@:�2 F {PRJLmRJB�~Ew A C+I(B�DG~EMOB<F k?F {PFJL(B<F K(FB<F?k :mFJB<k;:mF�Hcy ~EA(A FJwOwlFxF?HWQ wlF �P*98 ' ��2 � ��T�� P* % c ~ELmH�I(L w ~EL({ ~E{PF|kJw ~+H<HWM1_ ImF3k?C/2L2 F*� ~?Nf~H�(k?FJw ~oHWI(A(A CfH<F{PRJLmRJB�~EwlF32 FJL QvK(F3kJB<R?FJB�I(LmF3A(MOwlF3C$; C+L LmC+Q<Fvwzy RJQ�~EQ;k?C+I(B�~EL Q;K(F3w ~ B<F?k?C+L(L ~EMlH<H�~ELmk?F � B 0J{fwlFxk;:mC+MlHWMlFxFJQA CfHWMOQWMlC+L Km~ELmH3w ~ A�:(B�~+H<F � d k : ~/_ ImF�DGC+MlH�_ I y C+L k :mC+MlH<MOQvI(LmF5B 0J{fwlF�� FJQvwlC+B<H _ I y C+L�~EBWBWMONPF d I(L R?k;:mF?kK y ~EA(A ~EBWMlF32 FJL Q�� d B<FJNPFJL(MOB.~EI k?C+L Q<Fh4qQ<F FJL H<C/2L2 FJQ0K(F3A(MOwlF|A C+I(B Dz~EMOB<FxI(L ~EI(QWB<F|k;:mC+My4 %

<�FJBWQ�~EMOLmHow ~EL({ ~E{PF?H MOLmkJwOImFJL Q K(F?H5DGC+LmkJQWMlC+L(L ~EwOMOQ<R?H K(F k?F {PFJL(B<F %�. B<C+wlC+{�� A ~EB Fh4(F32 A(wlF��k :mFJB<k;:mFd K(R32 C+L QWB<FJB I(L k?FJBWQ�~EMOL ((I(Q FJL I(QWMOwOMlH�~EL Q K(F?H B 0J{fwlF?H K y MOL DGRJB<FJLmk?F?H��FJQ MOw.I(QWMOwOMlH�F L ~EQWMONPF32 FJL Q wlFB<FJQ<C+I(B.~EBWBWM10JB<F�A C+I(B;k;:mFJB<k :mFJB � K(F+2 ~EL(M10JB<F�~+HWQWImkJMlFJImH<F � A ~EB@2 M Q<C+I(Q<F?H;wlF?H;H�R _ ImFJLmk?F?H.K y ~EA(A(wOMlkc~EQWMlC+LK(F?HvB 0J{fwlF?H3K y MOL D RJB<FJLmk?F?H�� k?FJwOwlF?H�_ I(M�A FJB@2 FJQWQWB<C+L Q|K(F5K(R32 C+L QWB<FJB|wlF=((I(Q % p w F?HWQvQ<C+I(Q d DG~EMOQvA CfH<HWM'((wlFK y I(QWMOwOMlH<FJB . B<C+wlC+{ A C+I(B5A(B<C+{fB�~�2L2 FJBoI(LmF K(F?H<k?FJL Q<F B<R?kJI(B<H<MONPF LmC+L5�zA(B<R?K MlkJQWMONPF�� FJQ ~EMOLmHWM ( RJLmRh\ kJMlFJBK I 2 R?kc~EL(MlH@2 F�K(FxB<FJQ<C+I(B.~EBWBWM10JB<FxL ~EQWM D�K(Fxk?Fxw ~EL({ ~E{PF %

6�] <�C+LmHWQWBWImkJQWMlC+L K(F?H0~EL ~Ew'A H<FJI(B<H�A C+I(B;{fB�~�2L2 ~EMOB<F?H;LmC+L5� k?C+L Q<Fh4qQWImFJwOwlF?H

�,�� Kl!GU nH� "� ��Q��l&MÌ"�Q�� !�

X� �(A C+I(B;Q<C+I(Q0H@AB2,( C+wlFxK(Fxw ~5{fB�~�2L2 ~EMOB<F X ,

� n M X F?HWQ�I(L Q<FJB@2 MOL ~Ew � ~EwlC+B<H �� !� X � 7 9 X ; %� n M X → ε F?HWQ�I(LmFxA(B<CqK ImkJQWMlC+LM� ~F�WC+I(Q<FJB ε

d�� !�X�h%

� n M X F?HWQxI(L#LmC+L5�zQ<FJB@2 MOL ~Ew�FJQ,_ ImF X → Y1Y2...YkF?HWQ3I(LmF A(B<C K ImkJQWMlC+LM�O2 FJQWQWB<F a Km~ELmH� �� !�

X� Hcy MOw Fh4 MlHWQ<F i � 0 ≤ i < k Q<FJwU_ ImF ε ∈

� �� !�Yj� A C+I(B 0 ≤ j < i FJQ a ∈� �� !�

Yi�h%

� �� !�X1X2...Xn

� �mA C+I(B�I(LmF|H�R _ ImFJLmk?FxK(F|H A!2=( C+wlF?H XiK(F3w ~o{fB�~�2L2 ~EMOB<F=,

$&%∀a ∈

� �� !�X1

� FJQ a F?HWQ�I(L Q<FJB@2 MOL ~Ew � ~F�[C+I(Q<FJB a Km~ELmH �� !� X1X2...Xn�h%

�5%i ,87 $

75% MP��QM �OGU�ε ∈

� �� !�Xi� FJQ i < n

� ��IK��]�%

∀a ∈�� !�

Xi+1

� � ~F�WC+I(Q<FJB a Km~ELmH �� !� X1X2...Xn�h%

-5%i ,87 i � $

ST�65% �Ì

ε ∈� �� !�

Xi� � 1 ≤ i ≤ n

�� "��CB% ~F�WC+I(Q<FJB ε Km~ELmH �� !� X1X2...Xn

�h%�,�� Kl!GU nH� "� ��Q��l&MÌ"�Q�� ! "#�$ �&%('�)�*,+

A - A C+I(B;Q<C+ImH�wlF?H�LmC+L5�zQ<FJB@2 MOL ~EI54 A K(F3w ~o{fB�~�2L2 ~EMOB<F=,� ^ FJQWQWB<F/. Km~ELmH #�$ �&%0'1)�*,+ S - � C$; S F?HWQvwzy ~F4 MlC/2 F K(F w ~ {fB�~�2L2 ~EMOB<F FJQ2.owlF=2 ~EB _ ImFJI(B3K(F\mL K(Fxw ~ok : ~FElLmF K y FJL QWB<R?F %

� n y MOw�A ~5I(LmFxA(B<CqK ImkJQWMlC+L A→ αBβ � wlFxk?C+L Q<FJL I K(F �� ,+ β - Fh4(k?FJA(Q<R ε F?HWQ0~F�WC+I(Q<R d#�$ �3%0'�)�*,+B - %

� n y MOw Fh4qMlH<Q<F I(LmF A(B<CqK ImkJQWMlC+L A → αB C+II(LmF A(B<CqK ImkJQWMlC+L A → αBβ Q<FJwOwlF _ ImF� �� ,+

β - k?C+L QWMlFJL Q ε� kfy F?HWQ � d � K MOB<F β

∗⇒ ε

� �EwlF?H RJwlR32 FJL Q<H�K(F #�$ �3%0'�)�*,+ A - H<C+L Q�~F�WC+I(Q<R?Hd #�$ �3%0'�)�*,+B - %

�� 65% � � < ~EwlkJI(w�K(F?H�DGC+LmkJQWMlC+LmH � �� FJQ #�$ �3%0'�)4* %

j y MOLmk?C+L NPRJL(MlFJL Q K(F wzy ~EA(A(B<Cqk :mF LmC+L5�zA(B<R?K MlkJQWMONPF FJQ5w ~ B<FJw ~EQWMONPF MOLmF>G kc~+kJMOQ<R K(F w ~ B<F?k :mFJB<k;:mF A ~EBB<FJQ<C+I(B�~EBWBWM10JB<F %FX wOwlF�L y F?HWQ K(C+Lmk�~EA(A(wOM1_ ImR?F _ ImF�Km~ELmH�K(F?H)kc~+H�C$;5wlF?H)k : ~FElLmF?H d ~EL ~Ew'A H<FJB H<C+L Q)B<FJw ~EQWMONPFh�2 FJL Q�A FJQWMOQ<F?H�FJQ C$;�C+L5k :mFJB<k :mF d A(B<C+{fB�~�2L2 FJB�QWB 0?H B�~EA(MlK(F32 FJL Q�K(F?H ~EL ~Ew'A H<FJI(B<HH_ I(M+DGC+LmkJQWMlC+L(LmF32 FJL QA C+I(B;K(F?H;{fB�~�2L2 ~EMOB<F?H�_ I(M LmF|H<C+L Q;A ~+H�QWB 0?H ((MlFJL k?C+LmK MOQWMlC+L(LmR?F?H0A C+I(B;wlF?H0~EI(QWB<F?H 2 RJQ@:mCqK(F?H %

� ��`lm�!�QMP� �FE!l�GU�F�Ì �Q� kU��E�n�I"l&MÌ ��. C+I(BvA(B<C+{fB�~�2L2 FJB0I(LmF K(F?H<k?FJL Q<F�B<R?kJI(B<HWMONPF|A(B<R?K MlkJQWMONPF�� MOw Dz~EI(Q0K y ~�( C+B<K QWB�~?Nf~EMOwOwlFJB.HWI(B0w ~o{fB�~�2 �

2 ~EMOB<F K(F�2 ~EL(M10JB<F d K(RJQ<FJB@2 MOLmFJB wlF?H5kJBWMOQ 0JB<F?H K(F k;:mC+My4 K(F?HoB 0J{fwlF?H K(F A(B<CqK ImkJQWMlC+L d k;: ~/_ ImF DGC+MlH_ I y C+L K(C+MOQ�B<F32 A(w ~+k?FJB�I(L LmC+L5�zQ<FJB@2 MOL ~Ew A ~EB wzy I(LmF.K(F3H<F?H�A ~EBWQWMlF?H�K B<C+MOQ<F?H�K(F0B 0J{fwlF?H�K(F.A(B<CqK ImkJQWMlC+L %psw Hcy ~E{fMOQ%K(C+Lmk.K(F0H�~cNPC+MOB>_ ImFJw F?HWQ�w ~xH�R _ ImFJLmk?F.K(F?H�A(B<F32 MlFJB<H�H@A!2=( C+wlF?H%Q<FJB@2 MOL ~EI54p_ I(M A FJI(Q �JQWB<F;FJL5�{PFJLmK B<R?F.A ~EB�k : ~/_ ImF;A ~EBWQWMlF.K B<C+MOQ<F.K(F0B 0J{fwlF0K(F�A(B<CqK ImkJQWMlC+L % nqFJwlC+L wlF;kc~+H�� C+L A FJI(Q%NPC+I(wlC+MOB�B<FJ{ ~EB<K(FJBI(LM� K(FJI54 �qQWB<C+MlH�C+I A(wOImH�H@AB2,( C+wlF?H�K(F0A(B<R?K MlkJQWMlC+L %�X L A(B�~EQWM1_ ImF�� C+L H<F.k?C+L Q<FJL Q<F|H�C+I(NPFJL Q;K(FvQWB�~EMOQ<FJBwlF?H�{fB�~�2L2 ~EMOB<F?H _ I(M A FJI(NPFJL Q �JQWB<F�~EL ~Ew'AqH�R?FxA(B<R?K MlkJQWMONPF32 FJL Qx~?NPF?kxI(L H<FJI(w H@AB2,( C+wlF|K(F3A(B<RJN MlH<MlC+L %

. C+I(B�I(LmF�{fB�~�2L2 ~EMOB<F G _ I(M L y F?HWQ)A ~+H)B<R?kJI(B<HWMONPF d { ~EImk;:mF��+I(L ~EL ~Ew'AqH<FJI(B A ~EB K(F?H<k?FJL Q<F B<R?kJI(B<H<MONPFA(B<R?K MlkJQWMONPF H<F5k?C+LmHWQWBWI(MOQxK(C+Lmk FJL#kc~EwlkJI(w ~EL Q|K y ~�( C+B<K wlF?H.D C+LmkJQWMlC+LmH �� FJQ #�$ �3%0'�)�* Q<FJw�_ ImFk?FJw ~'F?HWQ K(R?kJBWMOQ d w ~�\m{fI(B<F 65% �5% j ~ DGC+LmkJQWMlC+L � �� wlC+B<H _ I y ~EA(A(wOM1_ ImR?F d I(LmF#H<R _ ImFJLmk?F�K(F

65% �L[ L ~Ew'AqH�FxK(F?H<k?FJLmKm~EL Q<F 6&-

H@AB2,( C+wlF?H��qB<FJQ<C+I(BWLmFxwlF3A(B<F32 MlFJB;H@AB2,( C+wlF3Q<FJB@2 MOL ~Ew K(Fvw ~5A�:(B�~+H<FxFJL({PFJLmK B<R?FxA ~EB;k?FJQWQ<FxH<R _ ImFJLmk?FxK(FH@AB2,( C+wlF?H % j ~.DGC+LmkJQWMlC+L #�$ �&%0'1)�* �+wlC+B<H _ I y ~EA(A(wOM1_ ImR?F d I(L H@AB2,( C+wlF�LmC+L5�zQ<FJB@2 MOL ~Ew � B<FJQ<C+I(BWLmF Q<C+ImH wlF?HQ<FJB@2 MOL ~EI54 _ I(M A FJI(NPFJL Q0HWI(MONqB<Fxk?F|H@AB2,( C+wlFxKm~ELmH;I(LmF3A(B<C+Q<C+A�:(B�~+H<F FJL({PFJLmK B<R?F|A ~EB;w ~5{fB�~�2L2 ~EMOB<F %t LmF.DGC+MlH�k?F?H�DGC+LmkJQWMlC+LmH�kc~EwlkJI(wlR?F?H��(C+L kJB<R?FxK(F?H A(B<Cqk?R?K I(B<F?H�K(F.B<F?k?C+L(L ~EMlH�H�~ELmk?FxA C+I(B k;: ~+kJI(L K(F?H

H@AB2,( C+wlF�LmC+L5�zQ<FJB@2 MOL ~EI54 K(F G% j F?H�A(B<C k?R?K I(B<F?H K(F�B<F?k?C+L(L ~EMlH<H�~ELmk?F�I(QWMOwOMlH<FJL Q I(L�Q�~�2 A C+LoK y FJL QWB<R?F ωFJQ)I(LmF�A(MOwlF K(F�H@AB2,( C+wlF?H�Q<FJB@2 MOL ~EI54 FJQ)LmC+L5�zQ<FJB@2 MOL ~EI54�� {PRJB<R?H)A ~EB wlF?H�QWB<C+MlH C+A RJB�~EQWMlC+LmH�HWI(MONf~EL Q<F?H ,

$&% } 5�&��u&w�(�2 - ,(HWM wlFxA(B<Cqk : ~EMOL Q<FJB@2 MOL ~Ew d B<F?k?C+L(L ~FElQWB<F Km~ELmH ω F?HWQ!2�� ~EwlC+B<H.k?F|H@AB2,( C+wlF&2 F?HWQB<FJQWMOB<R�K(F ω FJQ;F32 A(MOwlR�HWI(B�� %

�5% w&}�)�{`w�u�( @ � � - ,�K(RJA(MOwlF @ H@AB2,( C+wlF?H K I H<C/2L2 FJQ K(F'��FJQ F32 A(MOwlF wlF LmC+L5�zQ<FJB@2 MOL ~Ew � dwlFJI(B.A(w ~+k?F � w ~ A(B<C K ImkJQWMlC+L#~EA(A(wOM1_ ImR?F�B<R?K I(MOQvK(C+Lmk �8NPFJB<H0w ~ H<R _ ImFJLmk?F�K(F�H A!2=( C+wlF?H.K(RJA(MOwlR?H� w ~ A ~EBWQWMlF�K B<C+MOQ<F5K(F w ~ A(B<CqK ImkJQWMlC+L RJQ�~EL Qvk?C+LmHWQWMOQWImR?F5K(F?HvH@A!2=( C+wlF?HvK(RJA(MOwlR?H3Km~ELmH0wzy C+B<K B<F5K(FK(RJA(MOwlF32 FJL Q �h%

75% x!w ��!�5��{`| (�2 -&, B<FJQ<C+I(BWLmF|NqB�~EM HWM wlFxA(B<Cqk : ~EMOL Q<FJB@2 MOL ~Ew�Km~ELmH ω F?HWQ0RJ{ ~Ew d 2 FJQ Dz~EI54 H<MOLmC+L %<�F?H�A(B<Cqk?R?K I(B<F?H�K(Rh\mL(MlF?H��PMOw(DG~EI(Q%QWB�~EMOQ<FJB�k : ~/_ ImF;LmC+L5�zQ<FJB@2 MOL ~Ew K(F�w ~3{fB�~�2L2 ~EMOB<F0A C+I(B%A(B<C+{fB�~�2 �

2 FJB0wlF?H.A(B<Cqk?R?K I(B<F?H.K(F�B<F?k?C+L(L ~EMlH<H�~ELmk?F5k?C+BWB<F?HWA C+LmKm~EL Q<F?H %t. C+I(B3k : ~/_ ImF|A(B<CqK ImkJQWMlC+L A → α K(F�w ~{fB�~�2L2 ~EMOB<F�� C+L K(C+MOQ;kc~EwlkJI(wlFJB0wlF?H;H@AB2,( C+wlF?H;K(FxA(B<RJNqMlHWMlC+L ~+H�H<C kJMlR?H d k?FJQWQ<F|A(B<C K ImkJQWMlC+L ,

� �� %�� 1)(A→ α) =

{ �� (α) HWM ε 6∈ ��

(α)(� ��

(α)\{ε}) ∪#�$ �3%0'�)4*

(A) HWMOLmC+Lj ~.{fB�~�2L2 ~EMOB<F @ * * 3�� 98S* 3 2 d I(LmF�~EL ~Ew'AqH�F�K(F?H<k?FJLmKm~EL Q<F A(B<R?K MlkJQWMONPF Hcy MOwqFh4 MlHWQ<F ~EI=2 C+MOLmH�K(FJI54

A(B<CqK ImkJQWMlC+LmH A → α1FJQ A → α2

Q<FJwOwlF?H+_ ImF �� % �� ) (A → α1) ∩� �� %�� 1)

(A → α2) 6= ∅%

n M w ~ {fB�~�2L2 ~EMOB<F H<F5A(BP�JQ<F d I(LmFo~EL ~Ew'A H<FoK(F?H<k?FJLmKm~EL Q<F A(B<R?K MlkJQWMONPF�� A C+I(B3k;: ~/_ ImFoLmC+L5�zQ<FJB@2 MOL ~Ew �K(C+L Q3wlF?HvA(B<CqK ImkJQWMlC+LmHxH<C+L Q A → α1|...|αn

� R?kJBWMOB<F5I(LmF A(B<C k?R?K I(B<FoK(F B<F?k?C+L(L ~EMlH<H�~ELmk?F K(F w ~ DGC+B@2 FHWI(MONf~EL Q<F�,

kU��lmE�n�GU�F� B<F?k?C+L(L ~EMOQ � � �nUE �HG�M�FI∃ k ∈ �� % �� ) �

A→ α1

� Q<FJwO_ ImF�x!w �5��5��{`|�(<k�- �� "��~EA(A(wOM1_ ImFJB;w ~5A(B<C K ImkJQWMlC+L A→ α1�FI"�U��`I

∃ k ∈ � �� %�� 1) �A→ α2

� Q<FJwO_ ImF+x�w'�5�!��5{F|�(Wk�- �� "��~EA(A(wOM1_ ImFJB;w ~5A(B<C K ImkJQWMlC+L A→ α2%'%'%

�FI"�U��`I∃ k ∈ � �� %�� 1) �

A→ αn� Q<FJwU_ ImF�x!w �5��5��{`|�(<k�- �� "��

~EA(A(wOM1_ ImFJB;w ~5A(B<C K ImkJQWMlC+L A→ αn�FI"�U��K(R?kJwlFJLmk :mFJB.I(LmF|FJBWB<FJI(B0K(F|H A L Q�~F4 F %S��

. C+I(B ~EA(A(wOM1_ ImFJB5I(LmF A(B<CqK ImkJQWMlC+L K(F w ~ DGC+B@2 F A → X1...Xk��MOw�Dz~EI(Q A(B<CqK I(MOB<F I(LmF H<R _ ImFJLmk?F

K y RJLmC+Lmk?R?H e1, ..., ekK(F3w ~5DGC+B@2 F ,

ei =

{ } 5�/��u&w�( Xi- � HWM Xi

F?HWQ�I(L Q<FJB@2 MOL ~Eww�u5�(�&|�|��5{!� Xi

( - ��HWMOLmC+LA(I(MlH�C+L Q<FJB@2 MOLmF3A ~EB�I(L RJLmC+Lmk?R�w&} )�{`w�u�( � � - �%A C+I(B 2 ~EB _ ImFJB�w ~�B<F?k?C+L(L ~EMlH<H�~ELmk?FxK(Fvw ~ A ~EBWQWMlFK B<C+MOQ<F�K(F|w ~oA(B<C K ImkJQWMlC+L � HWM w ~ A(B<C K ImkJQWMlC+L F?HWQ0K(Fxw ~5DGC+B@2 F A→ ε � ~EwlC+B<H0wzy ~EA(A(wOMlkc~EQWMlC+L H<F3B<R?HWI�2 Fd w m} )�{`w5u ( Z � � - � �h%j y ~EL ~Ew'AqH�F A ~EB|K(F?H<k?FJL Q<F B<R?kJI(B<HWMONPF A(B<R?K MlkJQWMONPF F?H<Qvw ~ELmk?R?F FJL�~EA(A FJw ~EL Q�w ~ A(B<Cqk?R?K I(B<F K(FoB<F?k?C+L5�

L ~EMlH<H�~ELmk?F K(F wzy ~F4qMlC/2 F Km~ELmH I(L k?C+L Q<Fh4 Q<F C$;'w ~ A(MOwlF'� F?HWQ N MlK(F FJQ FJL k?C+LmHWMlK(RJB�~EL Q wlF A(B<F32 MlFJB

6&6 <�C+LmHWQWBWImkJQWMlC+L K(F?H0~EL ~Ew'A H<FJI(B<H�A C+I(B;{fB�~�2L2 ~EMOB<F?H;LmC+L5� k?C+L Q<Fh4qQWImFJwOwlF?H

H@AB2,( C+wlFxK(F ω k?C/2L2 F3wlF3A(B<Cqk : ~EMOL H@A!2=( C+wlF d B<F?k?C+L(L ~FElQWB<F % <�FJQWQ<F|~EL ~Ew'A H<F3B<RJImH<H<MOQ;HWM FJwOwlF3A ~EBWN MlFJL Q~EI ( C+I(Q;K(F ω FJL w ~EMlH<H�~EL Q;wzy ~F4qMlC/2 F�k?C/2L2 F|H<FJI(w H@AB2,( C+wlFxKm~ELmH;w ~5A(MOwlF %

� qO�!�Rk� "�� 'i <�C+LmHWMlK(RJB<C+LmH;w ~ {fB�~�2L2 ~EMOB<F|HWI(MONf~EL Q<F&,E → E � T | E � T | T

T → T � F | T � F | F

F → F�P | P

P → ( E - | N

N →�|�|�| � | � | � | � | � | � | �

c y ~�( C+B<K � C+L LmC+Q<F*_ ImFxk?FJQWQ<Fx{fB�~�2L2 ~EMOB<F�F?HWQ0B<R?kJI(B<HWMONPF d { ~EImk :mF % psw DG~EI(Q;RJwOM'2 MOLmFJBvH<F?H B<R?kJI(B<HWMONqMOQ<R?Hd { ~EImk :mF�� k?F*_ I(M LmC+ImH;K(C+L(LmF|w ~5{fB�~�2L2 ~EMOB<F R _ I(MONf~EwlFJL Q<F HWI(MON+~EL Q<F�,E → TX

X → � TX | � TX | ε

T → FY

Y → � FY | � FY | ε

F → PZ

Z →�PZ | ε

P → ( E - | N

N →�|�|�| � | � | � | � | � | � | �

X LmHWI(MOQ<F��kc~EwlkJI(wlC+LmH w ~ DGC+LmkJQWMlC+L �� A C+I(B Q<C+ImH wlF?H H@AB2,( C+wlF?H K(F w ~ {fB�~�2L2 ~EMOB<F %>. C+I(B wlF?HQ<FJB@2 MOL ~EI54 � � �� B<FJQ<C+I(BWLmFxwlF�H@A!2=( C+wlF3wOI(My� 2��32 F %�. C+I(B.wlF?H�LmC+L5�zQ<FJB@2 MOL ~EI54 � C+L C/((QWMlFJL Q�,

� �� (E) =

� �� (T ) = { ( , � , � , � , � , � , � , � , � , � , � }� ��

(X) = { � , � , ε}�� (T ) =

� �� (F ) = { ( , � , � , � , � , � , � , � , � , � , � }� ��

(Y ) = { � , � , ε}�� (F ) =

� �� (P ) = { ( , � , � , � , � , � , � , � , � , � , � }� ��

(Z) = {�, ε}��

(P ) = { ( , � , � , � , � , � , � , � , � , � , � }� �� (N) = {

�,�,�, � , � , � , � , � , � , � }

� L A ~+H<H<F5FJLmHWI(MOQ<Fo~EI kc~EwlkJI(w�K(F w ~ D C+LmkJQWMlC+L #�$ �3%0'�)�* A C+I(B3Q<C+ImHvwlF?HvLmC+L5�zQ<FJB@2 MOL ~EI54 K(F5w ~ {fB�~�2 �2 ~EMOB<F�,

#�$ �&%('�)�*(E) = {$} ∪ { - } = {$, - }#�$ �&%('�)�*(X) =

#�$ �&%('�)�*(E) ∪

#�$ �&%0'1)�*(X) = {$, - }#�$ �3%0'�)�*

(T ) =� ��

(X)\{ε} ∪#�$ �3%0'�)4*

(E) ∪#�$ �3%0'�)�*

(X) = { � , � , $, - }#�$ �&%0'1)�*(Y ) =

#�$ �&%('�)�*(T ) ∪

#�$ �3%0'�)�*(Y ) = { � , � , $, - }#�$ �3%0'�)�*

(F ) =� ��

(Y )\{ε} ∪#�$ �&%0'1)�*

(T ) ∪#�$ �3%0'�)�*

(Y ) = { � , � , � , � , $, - }#�$ �&%0'1)�*(Z) =

#�$ �&%('�)�*(F ) ∪

#�$ �3%0'�)�*(Z) = { � , � , � , � , $, - }#�$ �3%0'�)�*

(P ) =� ��

(Z)\{ε} ∪#�$ �&%0'1)�*

(F ) ∪#�$ �3%0'�)�*

(Z) = {�, � , � , � , � , $, - }

65% �L[ L ~Ew'AqH�FxK(F?H<k?FJLmKm~EL Q<F 6mC

� ��

��

� �� !��"��!�!�� #��$��!�%��'&!�'��(��*� �)� � �� !�� * ��,+.- ��(�� )�/�� 0�� !�� '&��!��1��2��(��*� �)�3��4��5 �� 6 �!� � �� !�� %�� %7��!��8�� 9�� 3��1&�� !6��3& �!��1��3��$��3&��'��!(��*� �� !�� %� ��:�6��;�

�� !�� 2�� & &�� =<(��* ��'�� * � � ��7 ��)>�

��? <@��(��*� �)�A+B�� %7�� !��-DC�C2�� * � � ��7 ��D> �� 7��E�E8�

F �� :�6 ��*�G�H��A�I�� A<KJ��!��D&�� !6�� $��LJ�>M�

FF

�� !�� N�� !� �� !?%� �!0��*�� O< ��* ��2��*�� %7 ��)>�

�%�� ;�

��? <@�� %7�� !��#PN��"��:!6��#> ��'C�<.��(��*� �)�A+B�� %7�� !��-DC�C2�� * � � ��7 ��)>Q�

F �� !? <@�%�� %7��!��C�C2�%� ��:�6��1R�R3��* � � �%7 ��4C�C�5�S�5T> ��'C3��;�

F �� 'C ? �� ;�

F��U��/�

F

�� !�� 2�� & ��&�� V< � ��3��:�6*��& W ��*��3� �� X ��*%��>�

� �� :�� !��=W � �

��? <@��:!6��&C�C3Y#> �? ��;< � C �� :�6��%��;� �2Z �� %7��!��V� ��[�[ > �

��(�� *� �)�A+ � -4C2��!(��*� ��A+ ��[�\ -]�F1�� !��&4� ?1? ��;<T>��!(��*� ��A+B�� 7��E�E�-^C2� �� X ��*%�V�� :�6*��E�EV�

F �� :�� UC2�� %7�� !��8�� 7�� [ C2��:!6��&8� �� &�"!� � ��4�� !6��

�� "��*�� 4� �2� �� '(��*%��!(��*� ��A+B�� 7��E�E�-^C2� �� X ��*%�V�

�� &�"�� '�� 1� �3(��!��*��U�� !��_�� !��

? ��;< � C1Y��`�� :�� !��UE � P �� :�6*��/� � E�E#> ��(�� *� �)�A+a�� %7��!��DE � -'C ��!(��*� ��A+B��:�� bE � -/�

F? ��;< � C \ � � P ��:�6��&8� � E�E#> �

��(�� *� �)�A+a�� :�6��%�� [3� -'C�5151�F�� :�6*��UCQ<.�� :�6*�� [ ��:�6��%��&)>3E \ �

FF

F'�� [�[�[�[�[�[�[�[�[�[�[�[�[�[�[�[�[�[�[�[�[�[�[�[�[�[�[�[�[�[�[�[�[�[�[�[�[�[�[�[�[�[�[�[�[�[ �� 1�� !��K��

�� 65%87 � c F?H<k?FJL Q<F|B<R?kJI(B<HWMONPF|A(B<R?K MlkJQWMONPF FJL � ~?Nf~ %

6� <�C+LmHWQWBWImkJQWMlC+L K(F?H0~EL ~Ew'A H<FJI(B<H�A C+I(B;{fB�~�2L2 ~EMOB<F?H;LmC+L5� k?C+L Q<Fh4qQWImFJwOwlF?H

<�F?H D C+LmkJQWMlC+LmH kc~EwlkJI(wlR?F?H��;C+L�QWB<C+I(NPFJB�~ d w ~ \m{fI(B<F 65%87 K(C+L(LmF#wlF?H K(Rh\mL(MOQWMlC+LmH B<FJw ~EQWMONPF?H d w ~{PF?HWQWMlC+L K(Fxw ~5A�:(B�~+H�FxFJQ;K(F3w ~5A(MOwlF % � L K(C+MOQ;FJL5\mL A ~+H<H<FJB d w ~5A(B<C+{fB�~�2L2 ~EQWMlC+L K(F?H�A(B<Cqk?R?K I(B<F?H0K(FB<F?k?C+L(L ~EMlH<H�~ELmk?F %�. C+I(B3w ~ A(B<Cqk?R?K I(B<FoK(F�B<F?k?C+L(L ~EMlH�H�~ELmk?F K(F N � wlF5K(R?kc~Ew ~E{PFoRJQ�~EL Q|HWA R?kJMy\�_ ImF d I(LQ<FJB@2 MOL ~Ew�K(C+L(LmR��w ~ A(B<Cqk?R?K I(B<F HWI(MONf~EL Q<F K(RJQ<F?kJQ<F w ~ B 0J{fwlF K(F A(B<CqK ImkJQWMlC+L d ~EA(A(wOM1_ ImFJB FJL NPRJBWMy\ FJBwlF A(B<F32 MlFJBoH A!2=( C+wlF K(RJBWMON+~�((wlF K(F k : ~+kJI(LmF K(F?H A ~EBWQWMlF?H K B<C+MOQ<F?HoK(F?H B 0J{fwlF?HoK(F A(B<C K ImkJQWMlC+L � C+L'~Dz~+kJQ<C+BWMlH<Rxw ~5B<R?K ImkJQWMlC+L d w ~ \mL K(Fxw ~5A(B<C k?R?K I(B<F � ,

�� !�� 2�� & �� 9A<T>�

�!? < �� !?%� �!0��*�� ,<�5 Y=5T>b> � &�� =<�5 Y=5T>M�F �� ? < �� !?%� �!0��*�� ,<�5 \ 5T>b> � &�� =<�5 \ 5T>M�F �� ? < �� !?%� �!0��*�� ,<�5 � 5T>b> � &�� =<�5 � 5T>M�F �� ? < �� !?%� �!0��*�� ,<�5��=5T>b> � &�� =<�5��=5T>M�F �� ? < �� !?%� �!0��*�� ,<�5�� 5T>b> � &�� =<�5�� 5T>M�F �� ? < �� !?%� �!0��*�� ,<�5��5T>b> � &�� =<�5��5T>M�F �� ? < �� !?%� �!0��*�� ,<�5��=5T>b> � &�� =<�5��=5T>M�F �� ? < �� !?%� �!0��*�� ,<�5�=5T>b> � &�� =<�5�=5T>M�F �� ? < �� !?%� �!0��*�� ,<�5�=5T>b> � &�� =<�5�=5T>M�F �� ? < �� !?%� �!0��*�� ,<�5��=5T>b> � &�� =<�5��=5T>M�F ��

:�6 �!��*�G�H��A�I�� ,< J��D&�� !6��$�� J�>Q� :�6 �!�� G� ��$ � � < \ >Q�F3�� !��&U� ? �� &�� < \ WU5 9A5T>^�

F

. C+I(B wlF LmC+L5�zQ<FJB@2 MOL ~Ew P � LmC+ImH ~?NPC+LmH K(FJI54 B 0J{fwlF?H K(F A(B<CqK ImkJQWMlC+L % j ~ A(B<F32 M10JB<F ~ k?C/2L2 FH@AB2,( C+wlF?H K(F A(B<RJNqMlHWMlC+L �� ( ( E - ) = { ( } %H. C+I(B5w ~ H�F?k?C+LmK(F B 0J{fwlF K(F A(B<CqK ImkJQWMlC+LM� C+L K(C+MOQB<F?k?C+L(L ~FElQWB<F.I(L LmC/2,((B<F.K y C$; �� (N) = {

�,�,�, � , � , � , � , � , � , � } % � L C/((QWMlFJL Q%w ~|A(B<C k?R?K I(B<FK(FxB<F?k?C+L(L ~EMlH<H^~ELmk?F�,

�� !�� 2�� & �� 08<T>�

�!? < �� !?%� ��0��* � � �,<�5�<�5T>#> �&�� =<�5�<�5T>M�� A<T>M�&�� =<�5T> 5T>M��&�� <��=WU5.0A5T> �

F �� ? < �� !?%� �!0��*�� ,<�5 Y=5T> �� ?%� ��0��* � � �,<�5 \ 5 >�� !?%� �!0��*�� ,<�5 � 5T> �� ?%� ��0��* � � �,<�5��=5 >�� !?%� �!0��*�� ,<�5�� 5T> �� ?%� ��0��* � � �,<�5��5 >�� !?%� �!0��*�� ,<�5��=5T> �� ?%� ��0��* � � �,<�5�=5 >�� !?%� �!0��*�� ,<�5�=5T> �� ?%� ��0��* � � �,<�5��=5 >#> �

�� 9A<T>M��&�� < \ WU5.0A5T> �

F �� :�6 �!��*�G�H��A�I�� ,< J��D&�� !6��$�� J�>Q� :�6 �!�� G� ��$ � � < \ >Q�

FF

. C+I(BowlF LmC+L5�zQ<FJB@2 MOL ~Ew Z ��C+L ~ K(FJI54�B 0J{fwlF?HoK(F A(B<CqK ImkJQWMlC+L %�. C+I(Bow ~ A(B<F32 M10JB<F��)C+L'~ k?C/2L2 FH@AB2,( C+wlF?H K(F A(B<RJN MlH<MlC+L � �� (�PZ) = {

�}%U. C+I(Bow ~ H�F?k?C+LmK(F B 0J{fwlF��w ~ A ~EBWQWMlF K B<C+MOQ<F F?HWQ ε �k?FJQWQ<F B 0J{fwlF�� LmF k?C+LmH<C/2L2 ~EL Q A ~+H K(F H@AB2,( C+wlF?H��)LmF Hay ~EA(A(wOM1_ ImFJL Qp_ ImF HWM wlF A(B<Cqk : ~EMOL H@AB2,( C+wlF d

B<F?k?C+L(L ~FElQWB<FxDz~EMOQ�A ~EBWQWMlF�K(F?H0HWI(MON+~EL Q<H;K(F Z �(K(C+Lmk { � , � , � , � , $, - } % � L C/((QWMlFJL QvK(C+Lmk�,�� !�� 2�� & �� =<T>�

�!? < �� !?%� ��0��* � � �,<�5�� 5T>#> �&�� =<�5�� 5T>M�� 0A<T>M�� =<T>M��&�� <��=WU5��=5T> �

F �� ? < �� !?%� �!0��*�� ,<�5�� 5T> �� ?%� ��0��* � � �,<�5 � 5 >�� !?%� �!0��*�� ,<�5 E=5T> �� ?%� ��0��* � � �,<�5 [ 5 >�� !?%� �!0��*�� ,<�5HS�5T> �� ?%� ��0��* � � �,<�5T> 5 >#> �

��&�� <HY=WU5��=5T> �

65% �L[ L ~Ew'AqH�FxK(F?H<k?FJLmKm~EL Q<F 6&W

F �� :�6 �!��*�G�H��A�I�� ,< J��D&�� !6��$�� J�>Q� :�6 �!�� G� ��$ � � < \ >Q�

FF

j ~.B<F?k?C+L(L ~EMlH<H�~ELmk?F K y I(L5DG~+kJQ<FJI(B)Dz~EMOQ�MOL Q<FJBWNPFJL(MOB�I(LmF�H�FJI(wlF%B 0J{fwlF K(F�A(B<C K ImkJQWMlC+LL_ I(MqHcy ~EA(A(wOM1_ ImF HWMwlF|A(B<Cqk : ~EMOL#H@AB2,( C+wlF d B<F?k?C+L(L ~FElQWB<F DG~EMOQ.A ~EBWQWMlF K(F � �� (PZ) = { ( , � , � , � , � , � , � , � , � , � , � } %� L ~oK(C+Lmk�,

�� !�� 2�� & �� V<T>�

�!? < �� !?%� ��0��* � � �,<�5�<�5T>�� ?%� ��0��* � � �,<�5HY=5 > �� !?%� ��0��* � � �,<�5 \ 5T>�� ?%� ��0��* � � �,<�5 � 5 > �� !?%� ��0��* � � �,<�5��5T>�� ?%� ��0��* � � �,<�5�� 5 > �� !?%� ��0��* � � �,<�5�� 5T>�� ?%� ��0��* � � �,<�5��=5 > �� !?%� ��0��* � � �,<�5��5T>�� ?%� ��0��* � � �,<�5�=5 > �� !?%� ��0��* � � �,<�5��5T>�> �� 0A<T>M�� =<T>M��&�� < � WU5�� 5T> �

F �� :�6 �!��*�G�H��A�I�� ,< J��D&�� !6��$�� J�>Q� :�6 �!�� G� ��$ � � < \ >Q�

FF

. C+I(B;w ~ B<F?k?C+L(L ~EMlH<H^~ELmk?FxK y I(L Y � C+L ~�QWB<C+MlH B 0J{fwlF?H0K(F.A(B<CqK ImkJQWMlC+L K(C+L Q�wlF?H�H A!2=( C+wlF?H�K(FvA(B<RJNqMy�HWMlC+LmH;H�C+L Q;B<F?HWA F?kJQWMONPF32 FJL Q � � � FJQ;wlF?H;HWI(MONf~EL Q<H.K(F Y �(K y C$; ,�� !�� 2�� & �� A<T>�

�!? < �� !?%� ��0��* � � �,<�5 � 5T>#> �&�� =<�5 � 5T>M�� <T>M�� A<T>M��&�� <��=WU5��A5T> �

F �� ? < �� !?%� �!0��*�� ,<�5 � 5T>b> �&�� =<�5 � 5T>M�� <T>M�� A<T>M��&�� <��=WU5��A5T> �

F �� ? < �� !?%� �!0��*�� ,<�5 E=5T> �� ?%� ��0��* � � �,<�5 [ 5 >�� !?%� �!0��*�� ,<�5HS�5T> �� ?%� ��0��* � � �,<�5T> 5 >#> �

��&�� <HY=WU5��A5T> �F ��

:�6 �!��*�G�H��A�I�� ,< J��D&�� !6��$�� J�>Q� :�6 �!�� G� ��$ � � < \ >Q�F

F

. C+I(B|wlFoLmC+L5�zQ<FJB@2 MOL ~Ew T � MOw�L y A ~ FJLmk?C+B<FL_ I y I(LmF H�FJI(wlF B 0J{fwlF K(C+L QxwlF?HxH@AB2,( C+wlF?H|K(F5A(B<RJN MlH<MlC+LH<C+L Q;wlF?H�A(B<F32 MlFJB<H0K(F F �(K y C$; ,�� !�� 2�� & �� <T>�

�!? < �� !?%� ��0��* � � �,<�5�<�5T>�� ?%� ��0��* � � �,<�5HY=5 > �� !?%� ��0��* � � �,<�5 \ 5T>�� ?%� ��0��* � � �,<�5 � 5 > �� !?%� ��0��* � � �,<�5��5T>�� ?%� ��0��* � � �,<�5�� 5 > �� !?%� ��0��* � � �,<�5�� 5T>�� ?%� ��0��* � � �,<�5��=5 > �� !?%� ��0��* � � �,<�5��5T>�� ?%� ��0��* � � �,<�5�=5 > �� !?%� ��0��* � � �,<�5��5T>�> �� <T>M�� A<T>M��&�� < � WU5�� 5T> �

F �� :�6 �!��*�G�H��A�I�� ,< J��D&�� !6��$�� J�>Q� :�6 �!�� G� ��$ � � < \ >Q�

FF

C/Z <�C+LmHWQWBWImkJQWMlC+L K(F?H0~EL ~Ew'A H<FJI(B<H�A C+I(B;{fB�~�2L2 ~EMOB<F?H;LmC+L5� k?C+L Q<Fh4qQWImFJwOwlF?H

j FxLmC+L5�zQ<FJB@2 MOL ~Ew X H<FxQWB�~EMOQ<F�K(F+2 ~EL(M10JB<F�HWM'2 MOw ~EMOB<F d Y FJQ Z% a B<C+MlH0B 0J{fwlF?H.K(FxA(B<CqK ImkJQWMlC+L C+L Q

A C+I(B;H@A!2=( C+wlF?H.K(F3A(B<RJN MlH<MlC+L B<F?HWA F?kJQWM D H � � ��FJQ;wlF?H0HWI(MON+~EL Q<H;K(F X �(K y C$;�� !�� 2�� & �� <T>�

�!? < �� !?%� ��0��* � � �,<�5HE�5T>#> �&�� =<�5HE�5T>M�� <T>M�� <T>M��&�� <��=WU5�� 5T> �

F �� ? < �� !?%� �!0��*�� ,<�5 [ 5T>b> �&�� =<�5 [ 5T>M�� <T>M�� <T>M��&�� <��=WU5�� 5T> �

F �� ? < �� !?%� �!0��*�� ,<�5HS�5T> �� ?%� ��0��* � � �,<�5T> 5 >#> ��&�� <HY=WU5�� 5T> �

F �� :�6 �!��*�G�H��A�I�� ,< J��D&�� !6��$�� J�>Q�:�6 �!��*�G� ��$ � � < \ >Q�

FF

X Q�FJL5\mLM� A C+I(B wlF.H A!2=( C+wlF E � MOw L y Ap_ I y I(LmFvB 0J{fwlF3K(F.A(B<C K ImkJQWMlC+L _ I(M Hay ~EA(A(wOM1_ ImF3HWM wlFvA(B<C k;: ~EMOLH@AB2,( C+wlF d B<F?k?C+L(L ~FElQWB<FxDz~EMOQ�A ~EBWQWMlF|K(F?H0A(B<F32 MlFJB<H0K(F T �(K y C$; ,�� !�� 2�� & �� A<T>�

�!? < �� !?%� ��0��* � � �,<�5�<�5T>�� ?%� ��0��* � � �,<�5HY=5 > �� !?%� ��0��* � � �,<�5 \ 5T>�� ?%� ��0��* � � �,<�5 � 5 > �� !?%� ��0��* � � �,<�5��5T>�� ?%� ��0��* � � �,<�5�� 5 > �� !?%� ��0��* � � �,<�5�� 5T>�� ?%� ��0��* � � �,<�5��=5 > �� !?%� ��0��* � � �,<�5��5T>�� ?%� ��0��* � � �,<�5�=5 > �� !?%� ��0��* � � �,<�5��5T>�> �� <T>M�� <T>M��&�� < � WU5 �A5T> �

F �� :�6 �!��*�G�H��A�I�� ,< J��D&�� !6��$�� J�>Q�:�6 �!��*�G� ��$ � � < \ >Q�

FF^ ~EMOL Q<FJL ~EL Q�� C+L A FJI(Q�QWB�~+k?FJB�wzy Fh4(R?kJI(QWMlC+L K I A(B<C+{fB�~�2L2 F0B<R?HWI(wOQ�~EL Q%H<I(B�I(LmF�Fh4qA(B<F?H<H<MlC+L � HWM'2 A(wlF��A C+I(B�LmFxA ~+H;H<F3LmC`APFJB.Km~ELmH�I(LmFxwlC+L({fImF|QWB�~+k?F � k?C/2L2 F � � �1,

Z �� A< >Z �� =<T>Z �� <T>Z �� 0A<T>Z �� 9 <T>Z &�� =<�5 � 5T>P3&�� =<�5 � 5T>� �� %�19 [!Z �P �� 9 <T>� �� 10 [!Z 9

P3�� 0A<T>Z �� =<T>

� �� [!Z P��!�� ZP3�� =<T>� ��%� �� %� � [!Z 0 �

P2�� <T>Z �� A<T>

� ��%� �� %� � [!Z P�� ZP2�� A<T>� �� %� � [�Z � �

P2�� =<T>Z �� =<T>Z &�� =<�5 E=5T>

65% �L[ L ~Ew'AqH�FxK(F?H<k?FJLmKm~EL Q<F CB$

P2&�� =<�5 E=5T>Z �� <T>Z �� <T>Z �� 0 <T>Z �� 9A<T>Z &�� =<�5��=5T>P2&�� =<�5��=5T>� �� %�19 [!Z �

P3�� 9A<T>� �� %�10 [!Z 9P �� 0 <T>Z �� <T>

� �� %� � [!Z P��!�� ZP �� <T>� �� [!Z 0 �

P3�� <T>Z �� A<T>

� �� [!Z P��!�� ZP3�� A<T>� ��%� �� %� � [!Z � �

P2�� <T>Z �� <T>

� ��%� �� %� � [!Z P�� ZP2�� <T>� �� %� � [�Z E � �

P2�� =<T>� �� %� � [!Z � �

P2�� A< >2

�� '� �� $�� $ � � ��'��

j F?H0~EL ~Ew'A H<FJI(B<H�A ~EB0K(F?H<k?FJL Q<FxB<R?kJI(B<HWMONPFxA(B<R?K MlkJQWMONPF�H<C+L Q�B<FJw ~EQWMONPF32 FJL Q0Dz~+kJMOwlF?H;FJQ�A ~+H�QWB<C+A Dz~+HWQWMy�K MlFJI54 d k?C+LmHWQWBWI(MOB<F�H<M w ~o{fB�~�2L2 ~EMOB<F�F?HWQ�B<FJw ~EQWMONPF32 FJL Q.A FJQWMOQ<F % � L A FJI(Q;k?FJA FJLmKm~EL Q0wlFJI(B0B<FJA(B<C k;:mFJBI(LmFvI(QWMOwOMlH�~EQWMlC+L A FJI F>G kc~+k?F3K I Q<F32 AmH�FJQ K(Fvwzy F?HWA ~+k?F d kc~EImH�F.K(F?H�LmC/2,((B<FJI54 ~EA(A FJwlH�K(F 2 RJQ@:mCqK(F?H� k?F _ ImF wzy C+L A FJI(Q k?C+LmH<Q�~EQ<FJB Km~ELmH w ~ QWB�~+k?F K(F wzy Fh4(F32 A(wlF A(B<R?k?R?K(FJL Q � _ I(M;LmR?k?F?H�HWMOQ<FJL Q d w ~ DGC+MlHK I Q<F32 AmHxFJQvk?C+LmH<C/2L2 FJL QxA ~+H<H�~�((wlF32 FJL Q3K y F?H<A ~+k?F5Km~ELmHvw ~ A(MOwlFoK y Fh4 R?kJI(QWMlC+L#K I A(B<C+{fB�~�2L2 F %�X LHWI(MONf~EL Q�wzy I(L K(F?H�A(wOImH NqMlFJI54 Q@:mR?C+B 032 F?H;K(F3wzy MOL D C+B@2 ~EQWM1_ ImF�� d H�~cNPC+MOB)_ ImFvQ<C+I(Q0k?F�_ I(M A FJI(Q�H<FvDz~EMOB<FB<R?kJI(B<HWMONPF32 FJL Q A FJI(Q ~EImH�HWM�H<F DG~EMOB<F MOQ<RJB�~EQWMONPF32 FJL Q��MOw�F?HWQoA CfH�HWM'((wlF K(F k?C+LmHWQWBWI(MOB<F K(F?H ~EL ~Ew'A H<FJI(B<HA(B<R?K MlkJQWM DGH0LmC+L5�zB<R?kJI(B<HWM DGH�_ I(M I(QWMOwOMlH<FJL Q.wzy MOQ<RJB�~EQWMlC+L % j F�k;:mC+My4 K(F?H;B 0J{fwlF?H.K(FxA(B<C K ImkJQWMlC+L d ~EA(A(wOM1_ ImFJBd k : ~/_ ImF;RJQ�~EA F�K(F�K(RJBWMONf~EQWMlC+L H<F�Dz~EMOQ FJL I(QWMOwOMlH^~EL Q�I(LmF�Q�~�((wlF _ I(M �fRJQ�~EL Q�K(C+L(LmR�wlF�A(B<Cqk : ~EMOL H@AB2,( C+wlFd B<F?k?C+L(L ~FElQWB<F Km~ELmH|w ~ A�:(B�~+H<F FJQ|wlF LmC+L5�zQ<FJB@2 MOL ~Ew d B<R?K I(MOB<F�� B<FJQ<C+I(BWLmF w ~ B 0J{fwlF K(F A(B<CqK ImkJQWMlC+L dI(QWMOwOMlH<FJB %nqC+MOQ G I(LmF;{fB�~�2L2 ~EMOB<F.K(C+L Q�w ~3Q�~�((wlF;K y ~EL ~Ew'A H<F;F?HWQ � FJQ ω I(LmF;k;: ~FElLmF d ~EL ~Ew'A H<FJB��fwzy ~EwO{PC+BWMOQ@:�2 F

K y ~EL ~Ew'A H<F _ I(M A(B<C K I(MOQ I(LmFvK(RJBWMON+~EQWMlC+L d { ~EImk :mF3K(F ω FJL H<F�( ~+H^~EL Q�HWI(B�wlF.H<k;:mR32 ~5K(F0w ~,\m{fI(B<F 65% ]H<FxK(R?kJwOMOLmF|K(F|w ~ DG~$�?C+L H<I(MON+~EL Q<F�,$&%e. CfHWMOQWMlC+L(LmFJBvwlFxkJI(B<H<FJI(B0H<I(B�wlFxA(B<F32 MlFJB0H@AB2,( C+wlF|K(F ω

%�5% p L(MOQWM ~EwOMlH<FJB0w ~ pile ~?NPF?k|wzy ~F4qMlC/2 F|FJL D C+LmK K(FxA(MOwlF %75% MP��QM �OG�� w ~oA(MOwlF3L y F?HWQ;A ~+H;N MlK(FxFJQ;wzy FJL QWB<R?F ω L y F?HWQ�A ~+H0Q<FJB@2 MOLmR?F ��I"��]�% nqC+MOQ � wlF|H@AB2,( C+wlFxFJL H<C/2L2 FJQ0K(F3A(MOwlF�FJQ �owlF3A(B<Cqk : ~EMOL Q<FJB@2 MOL ~Ew d B<F?k?C+L(L ~FElQWB<F�Km~ELmH ω-5% �FI �7g� 7 . �� "��F�65% \mL FJQ0HWImk?k 0?H0K(Fxwzy ~EL ~Ew'AqH�FCB% �FI"�U��o�Ì �?7 � 6= .L��&w�~�5% K(RJA(MOwlFJB � FJQ;A ~+H<H<FJB0~EI A(B<Cqk : ~EMOL Q<FJB@2 MOL ~Ew�Km~ELmH ωW5% �FI"�U��o�Ì � F?HWQ;I(L LmC+L5�zQ<FJB@2 MOL ~EwT��/w�~$PZ5% �Ì � � � � � � 7 9 � → � � � ; ��&w�~

C � <�C+LmHWQWBWImkJQWMlC+L K(F?H0~EL ~Ew'A H<FJI(B<H�A C+I(B;{fB�~�2L2 ~EMOB<F?H;LmC+L5� k?C+L Q<Fh4qQWImFJwOwlF?H

Tampon d’entrée $b+a...

$XYZ

Pile

Programme d’analyseprédictive

Tabled’analyse M

flot de sortie

�� 65% ] � nqk :mR32 ~ K I A(B<C+{fB�~�2L2 F�K y ~EL ~Ew'A H<FxA(B<R?K MlkJQWMONPF

$&$&% K(RJA(MOwlFJB � FJQ0F32 A(MOwlFJB � � � FJQ �$ �5% M'2 A(BWM'2 FJB � → � � � HWI(B�wlF O �+Q;K(F|H<C+BWQWMlF~!{F| �&|$P75% FJBWB<FJI(B0K(F|H@AqL Q�~F4(F$3]�% �FI"�U��

$P-5% FJBWB<FJI(B0K(FxH@AqL Q�~F4(FS��

j y ~EwO{PC+BWMOQ@:�2 F K(F k?C+LmHWQWBWImkJQWMlC+L K(F w ~ Q�~�((wlF K y ~EL ~Ew'A H<F A(B<R?K MlkJQWMONPF MOQ<RJB�~EQWMONPF F?HWQoK(C+L(LmR d w ~ \��{fI(B<F 65%8-5% <�FJQ�~EwO{PC+BWMOQ@:�2 F3B<FJA(B<FJLmK F?H<H<FJL QWMlFJwOwlF32 FJL Q�wlF?H kJBWMOQ 0JB<F?H K(F.k;:mC+My4 K(F?H�B 0J{fwlF?H�K(F0A(B<CqK ImkJQWMlC+L_ ImF�LmC+ImH�~cNPC+LmH%I(QWMOwOMlH<R?H�Km~ELmH�w ~xK(F?H�k?FJL Q<F;B<R?kJI(B<H<MONPF;A(B<R?K MlkJQWMONPF��qFJL wlF?H�B<FJ{fB<C+I(A ~EL Q�Km~ELmH%I(LmF�Q�~�((wlF %� L�B<F?k?C+L(L ~FElQowlF kc~+H K(F?H5H@AB2,( C+wlF?H�A ~EB@2 M�wlF?H�A(B<F32 MlFJB<HoK(F w ~ A ~EBWQWMlF K B<C+MOQ<F K(F k : ~/_ ImF B 0J{fwlF K(FA(B<CqK ImkJQWMlC+LM�mA(I(MlH;k?FJwOI(M K(F3wzy ~EA(A(wOMlkc~EQWMlC+L K(F?H�B 0J{fwlF?H0A(B<C K I(MlH�~EL Q;w ~ k;: ~FElLmFxN MlK(F ε

%

� qO�!�Rk� "�� y� <�C+LmHWMlK(RJB<C+LmH d LmC+I(NPFc~EI w ~5{fB�~�2L2 ~EMOB<F�K(FxLmC+QWB<F�Fh4 F32 A(wlFxA(B<R?k?R?K(FJL Q�,E → TX F → PZ

X → � TX | � TX | ε Z →�PZ | ε

T → FY P → ( E - | N

Y → � FY | � FY | ε

N →�|�|�| � | � | � | � | � | � | �

j ~oQ�~�((wlF�K y ~EL ~Ew'AqH<F�C/((Q<FJL ImF d A ~EBWQWMOB.K(Fxwzy ~EwO{PC+BWMOQ@:�2 F�F?HWQ:,

65% �L[ L ~Ew'AqH�FxK(F?H<k?FJLmKm~EL Q<F C/7

nqC+MOQ�I(LmF {fB�~�2L2 ~EMOB<F G �+wzy ~EwO{PC+BWMOQ@:�2 F�A(B<CqK I(MOQ�I(LmF Q�~�((wlF�K y ~EL ~Ew'A H<F A(B<R?K MlkJQWMONPF M A C+I(B G �fHWMw ~0{fB�~�2L2 ~EMOB<F G F?HWQ j j � $��h%&. C+I(B�k?FJw ~H�+C+L HWI(A(A CfH<Fb_ ImF�wlF?H)D C+LmkJQWMlC+LmH �� FJQ #�$ �3%0'�)4*C+L Q0RJQ<RxA(B<Rc~Ew ~�((wlF32 FJL Qvkc~EwlkJI(wlR?F?H %$&% k �QG�� k : ~/_ ImF|A(B<CqK ImkJQWMlC+L A→ α

� ��IK��5% k �QG�� k : ~/_ ImFxQ<FJB@2 MOL ~Ew a Km~ELmH � �� ,+ α - � ��I"�F�75% ~F�[C+I(Q<FJB A→ α

dM [A, a]

%ST�

]�% �`Iε ∈

�� ,+α - �� K��F�-5% k ��GU� k;: ~/_ ImFxQ<FJB@2 MOL ~Ew b ∈

#�$ �&%('�)�*,+A - ��I"��65% ~F�WC+I(Q<FJB A→ α

dM [A, b]

%CB% �`I

$ ∈#�$ �&%0'1)�*,+

A - �� "��5% ~F�[C+I(Q<FJB A→ αd

M [A, $]%

S��ST�

W5% u ~EMOB<F K(Fxk : ~/_ ImF�FJL QWB<R?FxLmC+L5� K(Rh\mL(MlF�K(F M I(LmF|FJBWB<FJI(B %

�� 65%8- � <�C+LmHWQWBWImkJQWMlC+L K(F?H�Q�~�((wlF?H;K y ~EL ~Ew'A H<F j j � $��

� � � � �

EX X → � TX X → � TXTY Y → ε Y → ε Y → � FY Y → � FYFZ Z → ε Z → ε Z → ε Z → ε Z →

�PZ

PN

( - @ �

E E → TX E → TXX X → ε X → εT T → FY T → FYY Y → ε Y → εF F → PZ F → PZZ Z → ε Z → εP P → ( E - P → NN N → n

j ~ \m{fI(B<F 65%86 B<FJQWB�~+k?F�wzy ~EA(A(wOMlkc~EQWMlC+L K(Fxwzy ~EwO{PC+BWMOQ@:�2 F5K y ~EL ~Ew'AqH�F ~EI kc~+H.K(F|wzy Fh4 A(B<F?H<HWMlC+L � � � % j ~K(RJBWMONf~EQWMlC+L C/((Q<FJL ImF5F?HWQ!, E ⇒g

TX ⇒g

FY X ⇒g

PZY X ⇒g

�ZY X ⇒

g

�Y X ⇒

g

�X ⇒

g

�� TX ⇒

g�� FY X ⇒

g

�� PZY X ⇒

g

�� NZY X ⇒

g

�� ZY X ⇒

g

�� Y X ⇒

g

�� X ⇒

g

��

2

CF] <�C+LmHWQWBWImkJQWMlC+L K(F?H0~EL ~Ew'A H<FJI(B<H�A C+I(B;{fB�~�2L2 ~EMOB<F?H;LmC+L5� k?C+L Q<Fh4qQWImFJwOwlF?H

A(MOwlF ωc R?kJMlHWMlC+L

E��

� [ A(A(wOM1_ ImFJB E → TXXT

��

� [ A(A(wOM1_ ImFJB T → FYXY F

��

� [ A(A(wOM1_ ImFJB F → PZXY ZP

��

� [ A(A(wOM1_ ImFJB P → NXY ZN

��

� [ A(A(wOM1_ ImFJB N →�

XY Z� �

� �� c R?kc~EwlFJB �

XY Z � �� [ A(A(wOM1_ ImFJB Z → ε

XY � �� [ A(A(wOM1_ ImFJB Y → ε

X � �� [ A(A(wOM1_ ImFJB X → � TX

XT � � �� c R?kc~EwlFJB �

XT � � [ A(A(wOM1_ ImFJB T → FYXY F � � [ A(A(wOM1_ ImFJB F → PZXY ZP � � [ A(A(wOM1_ ImFJB P → NXY ZN � � [ A(A(wOM1_ ImFJB N → �

XY Z � � � c R?kc~EwlFJB �XY Z

� [ A(A(wOM1_ ImFJB Z → εXY

� [ A(A(wOM1_ ImFJB Y → εX

� [ A(A(wOM1_ ImFJB X → ε� [ k?k?FJA(Q<FJB

�� 65%86 � [ L ~Ew'AqH<F j j�� $�� LmC+L5�zB<R?kJI(B<HWMONPF K(Fxwzy Fh4qA(B<F?H�HWMlC+L � � 75%

�:� � = -;: �36 4-;6 /)4�= # -;=.@ 4

j y ~EL ~Ew'AqH�F K(F?H�k?FJLmKm~EL Q<F k?C+LmHWMlK�0JB<F w ~ A�:(B�~+H<F K(F { ~EImk :mF d K B<C+MOQ<F FJQ k :mFJB<k;:mF d A(B<CqK I(MOB<F I(LmFK(RJBWMONf~EQWMlC+L d { ~EImk;:mF FJL�A ~EBWQ�~EL QoK(F wzy ~F4 MlC/2 F A C+I(B ~EBWBWMONPFJB5RJNPFJL QWImFJwOwlF32 FJL Q d w ~ A�:(B�~+H<F FJL QWM10JB<F %<�FoDz~EMlH�~EL Q�� d k : ~/_ ImF RJQ�~EA F�� wzy ~EL ~Ew'A H<F K(F?H�k?FJLmKm~EL Q<F A(B<R?K MlkJQWMONPF k :mC+MlH<MOQ�wlF?H|B 0J{fwlF?H K(F A(B<CqK ImkJQWMlC+Ld ~EA(A(wOM1_ ImFJBxFJL H<FxDGC+LmKm~EL Q3I(L(M1_ ImF32 FJL Q|HWI(BvwlF�A(B<Cqk : ~EMOL � C+I wlF?H�_ ImFJw1_ ImF?HvA(B<C k;: ~EMOLmH � H@A!2=( C+wlF dB<F?k?C+L(L ~FElQWB<F�Km~ELmH0w ~5A�:(B�~+H<F %j y ~EL ~Ew'AqH�Fo~+H�k?FJLmKm~EL Q<FoA(B<Cqk 0?K(F5K(F 2 ~EL(M10JB<F K M ~�2 RJQWB�~EwlF32 FJL Q�C+A(A CfH�R?F %QX wOwlF A ~EBWQxK(F5w ~ A�:(B�~+H<Fd ~EL ~Ew'AqH�FJBoFJQok :mFJB<k;:mF d B<F32 C+L Q<FJB d wzy ~F4 MlC/2 F FJL B<R?K I(MlH�~EL Q I(LmF H<R _ ImFJLmk?F K(F H@AB2,( C+wlF?HoQ<FJB@2 My�

L ~EI54 FJQvLmC+L5�zQ<FJB@2 MOL ~EI54#Km~ELmH3w ~ A(B<C+Q<C+A�:(B�~+H<F k?C+I(B�~EL Q<FoNPFJB<H3wlF H A!2=( C+wlF5LmC+L5�zQ<FJB@2 MOL ~Ew�FJL A ~EBWQWMlF{ ~EImk :mF K y I(LmFoB 0J{fwlF K(FoA(B<C K ImkJQWMlC+L � k?F5B<F32 A(w ~+k?F32 FJL Q A(B<CqK I(MOQxw ~ A(B<C+Q<C+A�:(B�~+H<F A(B<R?k?R?Km~EL Q<F Km~ELmHw ~oK(RJBWMONf~EQWMlC+L K(F3w ~oA�:(B�~+H<F %j y ~EL ~Ew'AqH�F ~+H<k?FJLmKm~EL Q<F Nf~ k;:mFJB<k :mFJB d A(B<CqK I(MOB<F|I(LmF K(RJBWMON+~EQWMlC+L d K B<C+MOQ<F % j y MOL Q<RJBP�JQ3K(F�k?F k :mC+My4

F?HWQ�DGC+BWQ;HWM'2 A(wlF % <�C/2L2 F|C+L k?C+LmHWQWBWI(MOQ;w ~oK(RJBWMONf~EQWMlC+L FJL B<F32 C+L Q�~EL Q.K(F3w ~5A�:(B�~+H<F3NPFJB<H wzy ~F4 MlC/2 F|FJLk?C+LmHWMlK(RJB�~EL Q)w ~0A�:(B�~+H<F�K(F%{ ~EImk;:mF d K B<C+MOQ<F��!w ~;B 0J{fwlF�K(F%A(B<CqK ImkJQWMlC+LL_ ImF%wzy C+L5k;:mFJB<k :mF d k : ~/_ ImF�RJQ�~EA FF?HWQ;k?FJwOwlF+_ I(M ~EA(A ~EBWMlFxwlF?H;H@AB2,( C+wlF?H wlF?H�A(wOImH d { ~EImk :mF�A CfH�HWM'((wlF3Km~ELmH�w ~5A(B<C+Q<C+A�:(B�~+H<F|k?C+I(B�~EL Q<F % � IKm~ELmH�wlF%H<FJLmH LmC+B@2 ~EwqK(F%w ~;K(RJBWMONf~EQWMlC+LM�!k?FJw ~0k?C+BWB<F?HWA C+LmK5K(C+Lmk�~EI B<F32 A(w ~+k?F32 FJL Q�K I5K(FJBWL(MlFJB)H@AB2,( C+wlFLmC+L5�zQ<FJB@2 MOL ~Ew wlF;A(wOImH d K B<C+MOQ<F0Km~ELmH�w ~3A(B<C+Q<C+A�:(B�~+H<Fvk?C+I(B�~EL Q<F��qkfy F?HWQ � d � K MOB<F.wlF;A(wOImH d K B<C+MOQ<F0wlC+B<H _ ImFQ<C+I(Q�k?FJI54p_ I(M RJQ�~EMlFJL Q�FJLmk?C+B<F.A(wOImH d K B<C+MOQ<F0C+L Q�K(R � d RJQ<R;B<R?K I(MOQ<H�wlC+B<H%K(F?H�K(RJBWMON+~EQWMlC+LmH�A(B<R?k?R?K(FJL Q<F?H %� L k?C+LmH<Q�~EQ<F K(C+Lmkp_ ImF k?FJQWQ<F DG~$�?C+L K(F A(B<C k?R?K(FJB N+~ L ~EQWI(B<FJwOwlF32 FJL Q k?C+LmHWQWBWI(MOB<F I(LmF K(RJBWMON+~EQWMlC+L dK B<C+MOQ<F�� A(I(MlH _ I y FJL#k?C/2L2 FJL��c~EL Q�A ~EB3wlFoH@AB2,( C+wlFowlF5A(wOImH d K B<C+MOQ<FL_ I(M�H<F QWB<C+I(NPFowlF A(wOImH d { ~EImk;:mFKm~ELmHow ~ A(B<F32 M10JB<F A(B<C+Q<C+A�:(B�~+H<F wlC+B<H K(F w ~ k?C+LmHWQWBWImkJQWMlC+L K y I(LmF K(RJBWMON+~EQWMlC+L'FJL H<FJLmH5MOL NPFJB<H<F � NPFJB<Hwzy ~F4 MlC/2 F � �mC+L Nf~ ~EwOwlFJB;A FJI d A FJI NPFJB<H�wlF|A(wOImH d K B<C+MOQ<F|Km~ELmH;w ~5A(B<F32 M10JB<F�A(B<C+Q<C+A�:(B�~+H<F %

65%87L[ L ~Ew'AqH�F|~+H<k?FJLmKm~EL Q<F C/-

. C+I(B5k?C+LmHWQWBWI(MOB<F I(LmF K(RJBWMONf~EQWMlC+L d K B<C+MOQ<F FJL�H<FJLmH�MOL NPFJB<H<F��C+L�N+~�( ~Ew ~PAPFJB wlF?H�H@A!2=( C+wlF?H K(F w ~A(B<C+Q<C+A�:(B�~+H<F k?C+I(B�~EL Q<F K(F { ~EImk :mF d K B<C+MOQ<F K(Fp2 ~EL(M10JB<F d B<F?k?C+L(L ~FElQWB<F wlF A(wOImH�NqMOQ<F A CfH<HWM'((wlF I(LmFA ~EBWQWMlF�K B<C+MOQ<F K(F|B 0J{fwlF|K(F�A(B<C K ImkJQWMlC+L _ ImF|wzy C+L Nf~oA C+I(NPC+MOB.B<F32 A(w ~+k?FJB0A ~EBvH�~oA ~EBWQWMlF|{ ~EImk;:mF�A C+I(BC/((Q<FJL(MOBow ~ A(B<C+Q<C+A�:(B�~+H<F A(B<R?k?R?K(FJL Q<F Km~ELmH w ~ K(RJBWMONf~EQWMlC+L % a�C+I(Q5wlF A(B<C/((w1032 F B<R?HWMlK(F K(C+Lmk Km~ELmH5w ~B<F?k?C+L(L ~EMlH<H�~ELmk?F K(F3w ~oA ~EBWQWMlF|K B<C+MOQ<F|K(F|w ~ ( C+L(LmFxB 0J{fwlF�K(F3A(B<C K ImkJQWMlC+L %� qO�!�Rk� "�� 1# <�C+LmHWMlK(RJB<C+LmH;w ~ {fB�~�2L2 ~EMOB<F�,

S → � AB uA → A +�� | +B → }

p wOwOImHWQWB<C+LmH5wzy ~EL ~Ew'A H<F ~+H<k?FJLmKm~EL Q<F K(F w ~ k : ~FElLmF ω 7 ��+�+��}Bu % � L ( ~Ew ~EMlF w ~ A�:(B�~+H�F K(F { ~EImk :mFd K B<C+MOQ<F A C+I(B B<F?k?C+L(L ~FElQWB<F _ ImF wlF +'FJL H<F?k?C+LmK(F A CfHWMOQWMlC+L A FJI(Q �JQWB<F B<F32 A(w ~+k?R A ~EB A H<FJwlC+L w ~H<F?k?C+LmK(F B 0J{fwlF K(FoA(B<C K ImkJQWMlC+L K(F k?FoLmC+L5�zQ<FJB@2 MOL ~Ew % � L�C/((QWMlFJL Q5~EwlC+B<H�w ~ A(B<C+Q<C+A�:(B�~+H<F A(B<R?k?R?K(FJL Q<F� A +��}Bu % � L�B<F?k?C/2L2 FJLmk?F ~EwlC+B<H�A C+I(B H<F B<FJLmK B<F k?C/2 A(Q<F�_ ImF w ~ H<R _ ImFJLmk?F A +�� k?C+BWB<F?H<A C+LmK d w ~A ~EBWQWMlF3K B<C+MOQ<F.K(F.w ~�A(B<F32 M10JB<F.B 0J{fwlF3K(F.A(B<C K ImkJQWMlC+L HWI(B A

% � L B<F32 A(w ~+k?FvK(C+Lmkvk?FJQWQ<F3H<R _ ImFJLmk?F0A C+I(BC/((Q<FJL(MOB�w ~ A(B<C+Q<C+A�:(B�~+H<F3A(B<R?k?R?K(FJL Q<F � A }5u %B^ ~EMOL Q<FJL ~EL Q��mkfy F?H<Q�wlF�} FJL QWB<C+MlHWM1032 FvA CfHWMOQWMlC+L _ I(M A FJI(Q�JQWB<F B<F32 A(w ~+k?R A ~EB B A C+I(B C/((Q<FJL(MOB � AB u % f C+ImH ~?NPC+LmH ~EwlC+B<H w ~�A ~EBWQWMlF K B<C+MOQ<F K(F w ~#B 0J{fwlF K(FA(B<CqK ImkJQWMlC+L K(F3wzy ~F4 MlC/2 F S �(k?F*_ I(M LmC+ImH;A FJB@2 FJQ;K y C/((Q<FJL(MOB S

%�X L B<R?HWI�2 R��mC+L ~ ,� + +��F}5u ⇐

d

� A +�� }Bu ⇐d

� A } u ⇐d

� AB u ⇐d

S 2

f C+ImH ~EwOwlC+LmH�NPC+MOB _ ImF0A C+I(B�I(LmF.kJw ~+H<H�F0K(F.{fB�~�2L2 ~EMOB<F?H LmC+L5� k?C+L Q<Fh4 QWImFJwOwlF?H�MOLmkJwOI ~EL Q�HWQWBWMlkJQ<F32 FJL QwlF?H {fB�~�2L2 ~EMOB<F?H j j � MOw F?H<Q�A CfH<HWM'((wlF3K(F.DG~EMOB<F3k?FJQWQ<F3B<F?k?C+L(L ~EMlH<H^~ELmk?FxFJL�( ~Ew ~PA ~EL Q;wlF?H�H A!2=( C+wlF?H�K(Fvw ~A ~EBWQWMlF3K B<C+MOQ<FxFJQ�FJL H<F3K(C+L(L ~EL Q�I(L LmC/2=((B<F�( C+BWLmR k K(F.H A!2=( C+wlF?H�K(FvA(B<R?K MlkJQWMlC+LmH�Km~ELmH w ~5HWI(MOQ<F3K(Fw ~ A(B<C+Q<C+A�:(B�~+H<Fxk?C+I(B�~EL Q<F|~EA(B 0?H wlF 2 ~ELmk :mF % <vy F?H<Q�~EMOLmH<Mt_ ImFvk?FJQWQ<F3~EA(A(B<Cqk :mFxK y ~EL ~Ew'A H<Fx~+H<k?FJLmKm~EL Q<FF?HWQ�~EA(A FJwlR?F LR(k) A C+I(B�� * �98 � 8 ' � ��T 4 8 <P2$@�@�TA@ '�� 8A4H* T @�3��8 � 3�� '�� H< T @&2 ��T 4 8U#�' 98 � * ��T �F2�8UT '$@TA@ �P* � * �� * � TU8A4 >"$#�%P'$) �'�� 3��(*��$TU<�8UTU'$@�� %

�� !#%� � � � ��'� � � � � �

n I(A(A CfH<C+LmH5I(LmF MOLmHWQ�~EL Q _ ImF wlF A(B<C/((w1032 F K(F B<F?k?C+L(L ~EMlH<H�~ELmk?F K(F w ~ A ~EBWQWMlF K B<C+MOQ<F K(F w ~ B 0J{fwlFK(F A(B<C K ImkJQWMlC+L d ~EA(A(wOM1_ ImFJBxF?HWQvB<R?H<C+wOI % j y ~EwO{PC+BWMOQ@:�2 F {PRJLmRJB�~Ew�K y ~EL ~Ew'A H<F ~+H<k?FJLmKm~EL Q<FoNf~ k?C+LmH<MlHWQ<FJBd ( ~Ew ~ APFJB5K(Fow ~ A(B<C+Q<C+A�:(B�~+H<F k?C+I(B�~EL Q<F K(Fo{ ~EImk;:mF d K B<C+MOQ<F FJQ d F32 A(MOwlFJB k?F?H|H@AB2,( C+wlF?HxQ�~EL Q,_ ImFwzy C+L L y ~ A ~+H ( ~Ew ~ APFJBvQ<C+I(Q<F�w ~ A ~EBWQWMlF5K B<C+MOQ<F K(F w ~ B 0J{fwlF5K(F�A(B<CqK ImkJQWMlC+L d ~EA(A(wOM1_ ImFJB % j C+B<H _ I y C+L#~B<F?k?C+L(L I#I(LmF5A ~EBWQWMlFoK B<C+MOQ<FoK(F5B 0J{fwlF5K(F A(B<CqK ImkJQWMlC+LM� C+L Nf~ wzy ~EA(A(wOM1_ ImFJB|FJL K(RJA(MOw ~EL Q|H<F?H3H@AB2,( C+wlF?HA C+I(BoF32 A(MOwlFJB d w ~ A(w ~+k?F wlF LmC+L5�zQ<FJB@2 MOL ~Ew0FJL A ~EBWQWMlF { ~EImk :mF K(F w ~+K MOQ<F B 0J{fwlF % n M C+L'A C+I(B<HWI(MOQ k?FA(B<Cqk?F?H<HWImH � ImH;_ I y d k?F _ ImF wzy ~F4 MlC/2 F H<C+MOQ F32 A(MOwlR FJQL_ ImF w ~ A�:(B�~+H�F ~EMOQ RJQ<R FJL QWM10JB<F32 FJL Qp( ~Ew ~PAPR?F��~EwlC+B<H w ~ A�:(B�~+H<F H<FJB�~ ~+k?k?FJA(Q<R?F % n M�C+L L y ~EBWBWMONPF A ~+H d B<F?k?C+L(L ~FElQWB<F I(LmF A ~EBWQWMlF K B<C+MOQ<F K(F B 0J{fwlF K(FA(B<CqK ImkJQWMlC+L C+I�FJLmk?C+B<F HWM�C+L�Q<FJB@2 MOLmF wlF?H�H@AB2,( C+wlF?H|K(Fow ~ A(B<C+Q<C+A�:(B�~+H�F k?C+I(B�~EL Q<F FJL#w ~EMlH<H�~EL Q|I(LmFA(MOwlF*_ I(M LmF|k?C+L QWMlFJL Q0A ~+H)_ ImFxwzy ~F4 MlC/2 F�� ~EwlC+B<H�w ~oA�:(B�~+H�FxF?HWQ;B<F �WFJQ<R?F %r0FJNPFJLmC+LmH�2 ~EMOL Q<FJL ~EL Q�~EIoA(B<C/((w1032 F�K(F w ~.B<F?k?C+L(L ~EMlH<H�~ELmk?F�K(F�w ~.A ~EBWQWMlF�K B<C+MOQ<F�K(F�w ~�( C+L(LmF�B 0J{fwlF

K(F A(B<C K ImkJQWMlC+L'Km~ELmH5w ~ A(B<C+Q<C+A�:(B�~+H�F k?C+I(B�~EL Q<F %�X L Q<FJB@2 F K(F NPC kc~�((I(w ~EMOB<F�� C+L A ~EBWwlF K(F #�2$@Q<>4 *A C+I(B;K(R?HWMO{fLmFJB.k?FJQWQ<FxA ~EBWQWMlF�K B<C+MOQ<F�,

�e��Ul U� - H<C+ImH � k : ~FElLmFvK y I(LmF.A(B<C+Q<C+A�:(B�~+H<F.K B<C+MOQ<F.K(F;w ~|{fB�~�2L2 ~EMOB<F _ I(M k?C+BWB<F?HWA C+LmK dw ~5A ~EBWQWMlF3K y I(LmF3B 0J{fwlFxK(FvA(B<CqK ImkJQWMlC+L K(C+L Q�wzy ~EA(A(wOMlkc~EQWMlC+L B<FJA(B<R?H�FJL Q<FxI(LmF3RJQ�~EA F3wlF.wlC+L({

C/6 <�C+LmHWQWBWImkJQWMlC+L K(F?H0~EL ~Ew'A H<FJI(B<H�A C+I(B;{fB�~�2L2 ~EMOB<F?H;LmC+L5� k?C+L Q<Fh4qQWImFJwOwlF?H

K y I(LmF�K(RJBWMON+~EQWMlC+L K B<C+MOQ<FxMOL NPFJB<H<F|A(B<C K I(MOQ<F d wzy ~EMlK(F|K(Fxk?FJQWQ<Fx{fB�~�2L2 ~EMOB<F %t L 2 ~ELmk;:mF�F?HWQ K(C+Lmk I(LmF#H<R _ ImFJLmk?F K(F#H A!2=( C+wlF?H Q<FJB@2 MOL ~EI548FJQ LmC+L5�zQ<FJB@2 MOL ~EI548~EMOLmH<M�_ ImF H�~A CfHWMOQWMlC+L Km~ELmH w ~ A(B<C+Q<C+A�:(B�~+H<F K B<C+MOQ<F % f C+QWB<F A(B<C/((w1032 F K(F B<F?k?C+L(L ~EMlH�H�~ELmk?F H�F B<R?HWI�2 F K(C+Lmk ~EIA(B<C/((w1032 F K(F5B<F?k?C+L(L ~EMlH<H�~ELmk?F K(F?H�2 ~ELmk :mF?H�Km~ELmH3wlF?H3A(B<C+Q<C+A�:(B�~+H�F?H�K B<C+MOQ<F?H3A(B<CqK ImkJQWM'((wlF?H d A ~EBWQWMOBK(F.w ~�{fB�~�2L2 ~EMOB<F % � L A ~EBWwlF3K y R>)W2� 2�6* K I�2 ~ELmk :mF3wlC+B<H _ I y C+L wlF0B<F32 A(w ~+k?F3A ~EB�w ~ A ~EBWQWMlFv{ ~EImk :mFxK(Fw ~5B 0J{fwlF|K(FxA(B<CqK ImkJQWMlC+L k?C+BWB<F?HWA C+LmKm~EL Q<F %j y MlK(R?F � ~+H�H<F�� {PRJL(M ~EwlF � K(F?H ~EL ~Ew'A H<F?H ~+H<k?FJLmKm~EL Q<F?H K I Q A A F j r F?HWQ K y ~?NPC+MOB B<F?k?C+L(L I _ ImF wlF?H

2 ~ELmk :mF?H K y I(LmF%{fB�~�2L2 ~EMOB<F�DGC+B@2 FJL Q FJL|B<Rc~EwOMOQ<R%I(L�w ~EL({ ~E{PF�B<RJ{fI(wOMlFJB��EFJQ A FJI(NPFJL Q)K(C+Lmk �JQWB<F�B<F?k?C+L(L ImHA ~EB�I(L ~EI(Q<C/2 ~EQ<FxK y RJQ�~EQ<Hb\mL(M % f C+ImH;~EwOwlC+LmH�NPC+MOB;Km~ELmH�wlF?H�H<F?kJQWMlC+LmH0HWI(MON+~EL Q<F?H�k?C/2L2 FJL Qvk?C+LmHWQWBWI(MOB<Fwzy ~EI(Q<C/2 ~EQ<F _ I(M%B<F?k?C+L(L ~FElQ k?F?H 2 ~ELmk :mF?H %�^ ~EMlH5H^~+k : ~EL QL_ ImF wlF?H 2 ~ELmk;:mF?H H<C+L Q5B<F?k?C+L(L ImHoA ~EBoI(L~EI(Q<C/2 ~EQ<F��mwzy ~EwO{PC+BWMOQ@:�2 F K y ~EL ~Ew'AqH�F3N+~H� A C+I(B;k : ~/_ ImF|RJQ�~EA F|K(FxK(RJBWMON+~EQWMlC+L MOL NPFJB<H<F��mk?C+LmH�C/2L2 FJB � FJQF32 A(MOwlFJB � wlF?H�H@AB2,( C+wlF?H)K(F�w ~0A(B<C+Q<C+A�:(B�~+H<F�k?C+I(B�~EL Q<F d wzy ~EMlK(F K(F�k?FJQ�~EI(Q<C/2 ~EQ<F��fFJQ�RJw ~E{fImFJB wlF 2 ~ELmk;:mFK�0?H)_ ImFxk?F|K(FJBWL(MlFJB0F?HWQ�B<F?k?C+L(L I %

� qO�!�Rk� "�� <�C+LmHWMlK(RJB<C+LmH d LmC+I(NPFc~EI w ~5{fB�~�2L2 ~EMOB<F|A(B<R?k?R?K(FJL Q<F=,S → � AB uA → A +�� | +B → }

j y ~EI(Q<C/2 ~EQ<F H<I(MON+~EL QxB<F?k?C+L(L ~FElQxwlF?H�2 ~ELmk :mF?H|Km~ELmHxwlF5A(B<C+Q<C+A�:(B�~+H<F?H�K B<C+MOQ<F?HxFJL({PFJLmK B<R?F?H|A ~EBxk?FJQWQ<F{fB�~�2L2 ~EMOB<F&,

?>=<89:;765401233

K(R3((I(Q // ?>=<89:;0a // ?>=<89:;1

b77

A ''

?>=<89:;4c // ?>=<89:;765401236

?>=<89:;2

b77

B ''d

��

?>=<89:;5e // ?>=<89:;765401237

?>=<89:;765401238

n M�C+L H<C+I�2 FJQ d k?FJQ3~EI(Q<C/2 ~EQ<F w ~ A(B<C+Q<C+A�:(B�~+H<FoK B<C+MOQ<F ��+�+��F}Bu��mwzy ~EI(Q<C/2 ~EQ<F N+~ K(F�wzy RJQ�~EQ Z d wzy RJQ�~EQ$ H<I(B�� A(I(MlH0NPFJB<H.wzy RJQ�~EQ 7 HWI(B +Q��_ I(M�F?HWQ.I(L RJQ�~EQvQ<FJB@2 MOL ~Ew)H<MO{fL ~Ew ~EL Q3wlF*2 ~ELmk;:mF + % c F*2��32 F�� HWMC+L#H<C+I�2 FJQxw ~ A(B<C+Q<C+A�:(B�~+H<Fp� � +��}Bu � wzy ~EI(Q<C/2 ~EQ<F Nf~ K(Fowzy RJQ�~EQ Z d $ HWI(B,� � A(I(MlH3NPFJB<H3wzy RJQ�~EQ 7 HWI(B� � A(I(MlH0NPFJB<H�wzy RJQ�~EQ ] HWI(B + FJQ0~EBWBWMONPF d w�� RJQ�~EQ)\mL ~Ew 6 HWI(B+� �(k?F,_ I(M HWMO{fL ~EwlF|wlF�2 ~ELmk :mF � +�� %

2

}�MlFJL H��(B�� MOw L y F?H<Q�A ~+H�LmR?k?F?H<H�~EMOB<FvK(F0B<FJA(B<FJLmK B<F3wlF�( ~Ew ~ A ~E{PFxK(F.w ~|A(B<C+Q<C+A�:(B�~+H�Fvk?C+I(B�~EL Q<F3K(FJA(I(MlHwlF K(R3((I(Qo~EA(B 0?H k;: ~/_ ImF RJw ~E{ ~E{PF % t L�RJw ~E{ ~E{PF A FJI(Q��JQWB<F NqI�k?C/2L2 F wlF DG~EMOQ K(F B<FJNPFJL(MOB FJL ~EBWBWM10JB<FKm~ELmH5wzy ~EI(Q<C/2 ~EQ<F=� ImH _ I y d wzy RJQ�~EQ ~EQWQ<FJMOL Q ~cN+~EL Q K(F k?C+LmH<C/2L2 FJBowlF?H5H@AB2,( C+wlF?H5K I 2 ~ELmk :mF��)A(I(MlH dF>/ F?kJQWImFJB�w ~vQWB�~ELmHWMOQWMlC+L HWI(B wlF LmC+L5�zQ<FJB@2 MOL ~Ew FJL A ~EBWQWMlF { ~EImk :mF0K(F w ~0B 0J{fwlF�K(F A(B<CqK ImkJQWMlC+L ~EA(A(wOM1_ ImR?F %. C+I(B�Dz~EMOB<F k?F k;:mF32 MOL FJL H<FJLmHxMOL NPFJB<H�F��C+L�I(QWMOwOMlH�F I(LmF MlK(R?F HWM'2 A(wlF , C+L F32 A(MOwlF wlF?H RJQ�~EQ<H5~EI#D I(BFJQ d 2 F?HWI(B<FxK(F?H QWB�~ELmHWMOQWMlC+LmH.FJL wlF?H MOL Q<FJB<kc~Ew ~EL Qx~?NPF?k3wlF?H�H@AB2,( C+wlF?H;Km~ELmH w ~5A(MOwlF %�[ MOLmHWM � RJw ~E{fImFJB;I(L2 ~ELmk :mF�Nf~�k?C+LmHWMlHWQ<FJB d K(RJA(MOwlFJB�~EI(Q�~EL Q K y RJQ�~EQ<H�_ ImF�K(F%H@AB2,( C+wlF?H)Km~ELmH wlF 2 ~ELmk :mF % <�F?kJM Nf~;K(R?k?C+I(NqBWMOB

65%87L[ L ~Ew'AqH�F|~+H<k?FJLmKm~EL Q<F C&C

FJL K(F?H<HWImHvK(F�A(MOwlF wzy RJQ�~EQ3~EQWQ<FJMOL Q|~?Nf~EL QxK(F�k?C+LmH<C/2 FJB3wlF=2 ~ELmk :mF�� RJQ�~EQ3K I�_ ImFJw)w ~ QWB�~ELmH<MOQWMlC+L HWI(BvwlFLmC+L5�zQ<FJB@2 MOL ~Ew�F32 A(MOwlR H<FJB�~ Dz~EMOQ %

. C+I(B 2 FJQWQWB<F|FJL �3I(NqB<Fxk?FJQ.~EwO{PC+BWMOQ@:�2 F|{PRJLmRJB�~Ew � C+L N+~oH<FvDGC+LmK(FJB0HWI(B;K(FJI54 Q�~�((wlF?H;K(F�K(R?kJMlHWMlC+L %t LmF.Q�~�((wlF Actions MOLmK M1_ ImF��mRJQ�~EL Q;K(C+L(LmR3wzy RJQ�~EQ;FJL H<C/2L2 FJQ;K(F3A(MOwlF3FJQ�wlFvA(B<Cqk : ~EMOL H@AB2,( C+wlFxKm~ELmHw ~xA(B<C+Q<C+A�:(B�~+H�Fvk?C+I(B�~EL Q<F3Hcy MOwmDz~EI(Q�F32 A(MOwlFJB k?F0K(FJBWL(MlFJB C+I FJLmk?C+B<FvRJw ~E{fImFJB�I(Lp2 ~ELmk :mF�_ I(M H<F0QWB<C+I(NPFFJL�H<C/2L2 FJQ K(FoA(MOwlF % t LmFoQ�~�((wlF Successeurs Nf~ MOLmK M1_ ImFJB�A C+I(Bxwzy RJQ�~EQ�FJL�H<C/2L2 FJQ�K(FoA(MOwlF FJQ|I(LLmC+L5�zQ<FJB@2 MOL ~Ew d F32 A(MOwlFJB��(NPFJB<H�_ ImFJw RJQ�~EQ;w ~5QWB�~ELmHWMOQWMlC+L K(C+MOQ;H<FvDG~EMOB<F�Km~ELmH�wzy ~EI(Q<C/2 ~EQ<F %

. wOImH A(B<R?kJMlH<R32 FJL Q��aH<C+MOQ G I(LmF�{fB�~�2L2 ~EMOB<F�K(F�w ~/_ ImFJwOwlF�K(F?H Q�~�((wlF?H�K y ~EL ~Ew'AqH<F Actions FJQ SuccesseursC+L Q RJQ<R0k?C+LmH<QWBWI(MOQ<F?H�FJQ ω I(LmF0k;: ~FElLmF d ~EL ~Ew'AqH�FJB��Pwzy ~EwO{PC+BWMOQ@:�2 F3HWI(MONf~EL Q%Nf~xA(B<CqK I(MOB<F;I(LmFvK(RJBWMONf~EQWMlC+Ld K B<C+MOQ<F�K(F w ,

$&%e. CfHWMOQWMlC+L(LmFJBvwlFxkJI(B<H<FJI(B0H<I(B�wlFxA(B<F32 MlFJB0H@AB2,( C+wlF|K(F ω$%

�5% p L(MOQWM ~EwOMlH<FJB0w ~ pile ~?NPF?k|wlF|H@AB2,( C+wlFxK(Fxwzy RJQ�~EQ;MOL(MOQWM ~Ew s0FJL DGC+LmK K(FxA(MOwlF %75% �FE!k EmMP�!�

]�% H�C+MOQ s wlFxH@AB2,( C+wlF|K y RJQ�~EQ0FJL H<C/2L2 FJQ.K(FxA(MOwlFxFJQ a wlFxA(B<C k;: ~EMOL H@AB2,( C+wlF|Km~ELmH ω$%

-5% �FIActions[s, a] F?HWQ (d, s′)

�� "��65% X 2 A(MOwlFJB a �(A(I(MlH s′ FJQ.~?Nf~ELmk?FJB;wlF|kJI(B<H<FJI(B;Km~ELmH ω$�FI"�U��C �Ì

Actions[s, a] F?H<Q (r,A→ β)�� "��

�5% c RJA(MOwlFJB 2× |β| H@AB2,( C+wlF?H;K(F3w ~oA(MOwlF %W5% nqC+MOQ s′ wlFxH@AB2,( C+wlF|K y RJQ�~EQ)2 ~EMOL Q<FJL ~EL Q3FJL H<C/2L2 FJQ0K(F3A(MOwlF %$PZ5% X 2 A(MOwlFJB A HWI(B�w ~oA(MOwlF %$&$&% X 2 A(MOwlFJB0wlFxH@AB2,( C+wlF|K y RJQ�~EQ Successeur[s′, A]%

�ÌJ�U��$ �5% �Ì

Actions[s, a] F?HWQ accepter�� "��

$P75% ~+k?k?FJA(Q<R=,87 �O�F��I�ÌJ��Q�

$3]�% c R?kJwlFJLmk :mFJBvI(LmFxFJBWB<FJI(B0K(F|H A L Q�~F4 F %$P-5%�� GU� �OG I'� ~+k?k?FJA(Q<R %

� qO�!�Rk� "�� Ks <�C+LmHWMlK(RJB<C+LmH;w ~ {fB�~�2L2 ~EMOB<F|K(F?H0Fh4 A(B<F?H<HWMlC+LmH0~EBWMOQ@:�2 RJQWM1_ ImF?H0H<I(MON+~EL Q<F�,E → E � T | T

T → T � F | F

F → ( E - | {F}t LmFxK(RJBWN+~EQWMlC+L K(F3w ~oA�:(B�~+H<F {F}

1 � {�} 2 � {�} 3K(C+L(LmFJB�~EMOQ;wOMlFJI ~EI54 ~+kJQWMlC+LmH0H<I(MON+~EL Q<F?H!,

C�� <�C+LmHWQWBWImkJQWMlC+L K(F?H0~EL ~Ew'A H<FJI(B<H�A C+I(B;{fB�~�2L2 ~EMOB<F?H;LmC+L5� k?C+L Q<Fh4qQWImFJwOwlF?H

. MOwlF X L QWB<R?F [ kJQWMlC+L. {F}

1 � {F} 2 � {�} 3.

.�{�}1 � {F} 2 � {�} 3

. K(R?kc~EwlFJB*{F}1. u � {F} 2 � {�} 3

. 2 ~ELmk :mF�� RJw ~E{fImFJB. a � {F} 2 � {�} 3

. 2 ~ELmk :mF�� RJw ~E{fImFJB. X � {F} 2 � {�} 3

. 2 ~ELmk :mF�� RJw ~E{fImFJB. X � {F}

2 � {�} 3. K(R?kc~EwlFJB �. X � {F} 2 � {�} 3. K(R?kc~EwlFJB*{F}

2. X � u � {�} 3. 2 ~ELmk :mF�� RJw ~E{fImFJB

. X � a � {�} 3. 2 ~ELmk :mF�� RJw ~E{fImFJB

. X � a � {�}3. K(R?kc~EwlFJB �. X � a � {�} 3. K(R?kc~EwlFJB*{F}

3. X � a � u . 2 ~ELmk :mF�� RJw ~E{fImFJB. X � a . 2 ~ELmk :mF�� RJw ~E{fImFJB. X . 2 ~ELmk :mF�� RJw ~E{fImFJB. X . ~+k?k?FJA(Q<FJB

2

a C+I(Q<F5w ~ K M0G kJI(wOQ<RoK(F?H 2 RJQ@:mC K(F?Hx~+H<k?FJLmKm~EL Q<F?H��t_ I(M�B<R?HWMlK(F Km~ELmH.w ~ A(BWMlH<F�K(F?HvK(R?kJMlHWMlC+LmH3K y ~EL ~F�w'A H<F � K(R?kc~EwlFJB��RJw ~E{fImFJB��~+k?k?FJA(Q<FJB � ��B<FJNqMlFJL Q d w ~�K(RJQ<F?kJQWMlC+L K Io2 ~ELmk :mF % j F?HN2 RJQ@:mCqK(F?H j r�H<C+L QDGC+LmK(R?F?H%HWI(B�wzy I(QWMOwOMlH^~EQWMlC+L K(F�Q�~�((wlF?H�K y ~EL ~Ew'AqH�F�_ I(M H<C+L Q�k?C+LmHWQWBWI(MOQ<F?H d A ~EBWQWMOB�K(F?H%{fB�~�2L2 ~EMOB<F?H % a B<C+MlH2 RJQ@:mCqK(F?H.H<C+L Q�2 ~EMOL Q<FJL ~EL QxA(B<C+A CfH<R?F?H��_ I(M K M0/�0JB<FJL QxF?H<H<FJL QWMlFJwOwlF32 FJL Q3A ~EB0wlFJI(Bvkc~EA ~+kJMOQ<R d QWB�~EMOQ<FJBK(F?H;kJw ~+H<H�F?H�A(wOImH;C+I 2 C+MOLmH0M'2 A C+BWQ�~EL Q<F?H0K(Fx{fB�~�2L2 ~EMOB<F?H0LmC+L5� k?C+L Q<Fh4 QWImFJwOwlF?H %

�� '� �'� � �� $ � ��

�,��U� MP�/G�lmMÌK�Q�onH��LMP� �� "��O�� <P'�# 3B)WR98S*��

�,��U� MP�/G�lmMÌK�Q�onH��LMP� �� "��p�� l��Q�UI��OGU��,��U� MP�/G�lmMÌK�Q�onH��LMP� �� "��p�>j��

65%87L[ L ~Ew'AqH�F|~+H<k?FJLmKm~EL Q<F C/W

nqC+MOQ G I(LmF {fB�~�2L2 ~EMOB<F��wzy ~EwO{PC+BWMOQ@:�2 F A(B<C K I(MOQ K(F?H�Q�~�((wlF?H K y ~EL ~Ew'AqH<F n j r Actions FJQSuccesseurs �0HWMxw ~ {fB�~�2L2 ~EMOB<F F?HWQ n j r %). C+I(B k?FJw ~H�;MOwxDz~EI(Q kc~EwlkJI(wlFJB w ~'k?C+wOwlF?kJQWMlC+L K(F?HFJLmH<F32,((wlF?H K y MOQ<F32 H n j r A C+I(B G ��A(I(MlH5w ~ D C+LmkJQWMlC+L #�$ �3%0'�)4* A C+I(B5k;: ~+kJI(L'K(F?H5H A!2=( C+wlF?HLmC+L5�zQ<FJB@2 MOL ~EI54 K(F G � FJQ0FJL5\mL k?C+LmHWQWBWI(MOB<F wlF?H;Q�~�((wlF?HvFJwOwlF?H � 2��32 F?H d A ~EBWQWMOB3K(F|k?FJQWQ<F�k?C+wOwlF?kh�QWMlC+L FJQ0K(Fxk?FJQWQ<F3DGC+LmkJQWMlC+L %�,�� J "��l&MÌ"�� nH��N�B��P�B��H "��pnJI1IKMP�!�� nqC+MOQ A → XY Z I(LmF B 0J{fwlF K(F A(B<CqK ImkJQWMlC+L K(F w ~ {fB�~�2L2 ~EMOB<F G ��I(L MOQ<F32 n j r�F?HWQ I(LmFA(B<C K ImkJQWMlC+L ~cNPF?k I(L A C+MOL Q B<FJA RJB�~EL Q I(LmF A CfHWMOQWMlC+L8Km~ELmH H^~�A ~EBWQWMlF#K B<C+MOQ<F % j F A C+MOL Q F?H<QI(QWMOwOMlH<R A C+I(BoMOLmK M1_ ImFJB w ~ A C+BWQWMlC+L K(F A ~EBWQWMlF K B<C+MOQ<F K(R � d B<F?k?C+L(L ImF Km~ELmHoI(LmF A(B<C+Q<C+A�:(B�~+H<FK B<C+MOQ<F � M % F % w ~ H<R _ ImFJLmk?FxK(F|H@AB2,( C+wlF?H;K(R � d B<F?k?C+L(L ImH �h%� k E!�F�5MÌ"�Q�

Fermeture(I)nqC+MOQ I I(L#FJLmH<F32,((wlF K y MOQ<F32 Hon j r!� w ~ DGFJB@2 FJQWI(B<F K(F I � LmC+Q<R?F Fermeture(I) � F?HWQ|C/((Q<FJL ImFA ~EB;wlF?H;K(FJI54 B 0J{fwlF?H0HWI(MONf~EL Q<F?H�,$&% psL(MOQWM ~EwlF32 FJL Q�� A(w ~+k?FJB0k : ~/_ ImFxMOQ<F32�K(F I Km~ELmH Fermeture(I)

%�5% n M [A → α • Bβ] F?H<Q Km~ELmH Fermeture(I) FJQ B → γ F?HWQ I(LmF A(B<C K ImkJQWMlC+L K(F G �~EwlC+B<H;~F�WC+I(Q<FJB�wzy MOQ<F32 [B → •γ]

dFermeture(I) Hcy MOw LmF.Hay A QWB<C+I(NPFvA ~+H�K(R � d % r0RJA RJQ<FJBwzy ~EA(A(wOMlkc~EQWMlC+L K(F�k?FJQWQ<F K(FJI54qM1032 F�B 0J{fwlFU� ImH;_ I y d k?Fb_ I y MOwqLmF H<C+MOQ�A(wOImH)A CfH<HWM'((wlF�K y ~F�[C+I(Q<FJB

K y MOQ<F32 H d Fermeture(I)%

� k E!�F�5MÌ"�Q�Transition[I,X]nqC+MOQ I I(L FJLmH<F32=((wlF�K y MOQ<F32 H;FJQ X I(L H@AB2,( C+wlF|K(F G �

$&% < ~EwlkJI(wlFJB I ′ � wzy FJLmH�F32,((wlF|K(F?H�MOQ<F32 H [A→ αX • β] Q<FJwlH)_ ImF3wzy MOQ<F32 [A→ α •Xβ] ∈ I%

�5%Transition[I,X] = Fermeture(I ′)

%�,�� J "��l&MÌ"�� nH��N�B��P�B��H "��pnJI1IKMP�!��N�� ,k �QG��

GnqC+MOQ G′ = (V ′, T, P ′, S′) w ~ {fB�~�2L2 ~EMOB<F ~EI({&2 FJL Q<R?F5C/((Q<FJL ImF K(F G = (V, T, P, S) FJL ~F�[C+I5�Q�~EL Q wlF0LmC+L5�zQ<FJB@2 MOL ~Ew S′d

V A C+I(B�C/((Q<FJL(MOB V ′ � w ~�A(B<C K ImkJQWMlC+L S′ → Sd

P A C+I(B�C/((Q<FJL(MOB P ′

FJQ0FJL B<F32 A(w ~$�c~EL Qvwzy ~F4qMlC/2 F S A ~EB S′ %$&% psL(MOQWM ~EwOMlH<FJB C ~EI H�FJI(w FJLmH<F32,((wlF�K y MOQ<F32 H;LmC+L5� 2 ~EB _ ImR�C/((Q<FJL I A ~EB

Fermeture({[S ′ → •S]})%

�5% MP��QM �OGU� MOw�Fh4qMlHWQ<FxK(F?H0FJLmH<F32,((wlF K y MOQ<F32 H;LmC+L5� 2 ~EB _ ImR?H0Km~ELmH C� ��I"�F�

75% nqC+MOQ I I(L FJLmH�F32,((wlF�K y MOQ<F32 H0LmC+L5� 2 ~EB _ ImR K(F C%

]�% k �QG�� k : ~/_ ImF|H@AB2,( C+wlFxK(Fx{fB�~�2L2 ~EMOB<F X ∈ V ∪ T� ��I"�F�

-5% �Ì MOw Fh4qMlHWQ<F3I(L MOQ<F32 [A→ α •Xβ] Km~ELmH I�� "��

65% n y MOw L y A F?HWQ�A ~+H;K(R � d � ~F�WC+I(Q<FJB Transition[I,X] k?C/2L2 F|FJLmH�F32,((wlFLmC+L5� 2 ~EB _ ImR d C%

ST� %ST� %

�� 65% C � <�C+LmHWQWBWImkJQWMlC+L K(F?H�Q�~�((wlF?H;K y ~EL ~Ew'A H<F n j r %

�&Z <�C+LmHWQWBWImkJQWMlC+L K(F?H0~EL ~Ew'A H<FJI(B<H�A C+I(B;{fB�~�2L2 ~EMOB<F?H;LmC+L5� k?C+L Q<Fh4qQWImFJwOwlF?H

�,��U� MP��GUl&M`I"�� nU�!�LMP� �� K�!�Nn Iy��U�� O�P� �O��Actions

�mMSuccesseursnqC+MOQ G′ I(LmF {fB�~�2L2 ~EMOB<F ~EI({&2 FJL Q<R?F�� wlF?H Q�~�((wlF?HoK y ~EL ~Ew'AqH�F n j r Actions FJQ SuccesseursH<C+L Q0C/((Q<FJL ImF?H0A ~EB:,

$&% <�C+LmHWQWBWI(MOB<F C = {I0, I1, ..., In}�mw ~ k?C+wOwlF?kJQWMlC+L K(F?H.FJLmH<F32=((wlF?H3K y MOQ<F32 H j r � Z � A C+I(B0w ~

{fB�~�2L2 ~EMOB<F G′ %�5% j y RJQ�~EQ i F?HWQ k?C+LmHWQWBWI(MOQ d A ~EBWQWMOB�K(F.wzy FJLmH<F32,((wlFxK y MOQ<F32 H Ii

% j F?H�~+kJQWMlC+LmH�K y ~EL ~Ew'AqH<F.A C+I(Bwzy RJQ�~EQ i H�C+L Q0K(RJQ<FJB@2 MOLmR?F?H.A ~EB�wlF?H�B 0J{fwlF?H0H<I(MON+~EL Q<F?H!,� ~ � n M [A→ α•aβ] ∈ Ii

�PH<M a ∈ T FJQ�H<M Transition[Ii, a] = Ij� ~EwlC+B<H Action[i, a] =�6R(<72$)W*�� j %

� ( � n M [A→ α•] ∈ Ii� ∀a ∈ Suivants(A), Action[i, a] = �PR�� T �P* par A→ α

%� k � n M [S′ → S•] ∈ Ii

�m~EwlC+B<H Action[i, $] = accepter%

n M�wlF?H3B 0J{fwlF?HxA(B<R?k?R?K(FJL Q<F?H�H<C+L Q3k?C+LHOmMlkJQWImFJwOwlF?H�� ~EwlC+B<Hxw ~ {fB�~�2L2 ~EMOB<F L y F?HWQxA ~+H�n j r FJQwzy ~EwO{PC+BWMOQ@:�2 F5R?k :mC+ImF %

75% n M A ∈ V FJQ Transition[Ii, A] = Ij~EwlC+B<H Successeurs[i, A] = j

%]�% a C+I(Q<F?H wlF?H FJL QWB<R?F?H LmC+L5� K(Rh\mL(MlF?H A ~EB wlF?H B 0J{fwlF?H FJL � � � FJQ � 7 � H<C+L Q A CfHWMOQWMlC+L(LmR?F?H d

* � �(* �� %-5% j y RJQ�~EQ MOL(MOQWM ~Ew0K(F wzy ~EL ~Ew'AqH�FJI(B F?HWQ k?FJwOI(M�_ I(M0~ RJQ<R k?C+LmHWQWBWI(MOQ d A ~EBWQWMOB K(F wzy FJLmH<F32,((wlFk?C+L Q<FJL ~EL Q.wzy MOQ<F32 [S′ → •S]

%

�� 65% � � <�C+LmH<QWBWImkJQWMlC+L K(F?H�Q�~�((wlF?H.K y ~EL ~Ew'AqH<F5n j r � HWI(MOQ<F �h%

65%87L[ L ~Ew'AqH�F|~+H<k?FJLmKm~EL Q<F �5$

nqC+MOQ G I(LmF8{fB�~�2L2 ~EMOB<F�� wzy ~EwO{PC+BWMOQ@:�2 F A(B<CqK I(MOQ K(F?H Q�~�((wlF?H K y ~EL ~Ew'A H<F j r Actions FJQSuccesseurs �%HWM�w ~ {fB�~�2L2 ~EMOB<F F?HWQ j r � $��h% . C+I(B k?FJw ~H��MOw�Dz~EI(Q kc~EwlkJI(wlFJB w ~#k?C+wOwlF?kJQWMlC+L K(F?HFJLmH<F32,((wlF?H�K y MOQ<F32 H j r � $�� A C+I(B G �fA(I(MlH�k?C+LmHWQWBWI(MOB<F0wlF?H�Q�~�((wlF?H%FJwOwlF?H � 2��32 F?H d A ~EBWQWMOB%K(F;k?FJQWQ<Fk?C+wOwlF?kJQWMlC+L %�,�� J "��l&MÌ"�� nH��N�B��P�B��H "��pnJI1IKMP�!��N�� h �nqC+MOQ A → XY Z I(LmF B 0J{fwlF K(F A(B<CqK ImkJQWMlC+L K(F w ~ {fB�~�2L2 ~EMOB<F G � I(L'MOQ<F32 j r � $�� F?HWQ I(LMOQ<F32 j r � Z � ~EI�_ ImFJw)F?HWQ0~F�WC+I(Q<R|I(L FJLmH<F32=((wlF�K(F H@A!2=( C+wlF?H0Q<FJB@2 MOL ~EI54 {a1, ..., an}

A C+I(Nf~EL QHWI(MON B<F|wlF|LmC+L5�zQ<FJB@2 MOL ~Ew A Km~ELmH0I(LmF|A(B<C+Q<C+A�:(B�~+H<F5K B<C+MOQ<F�C/((Q<FJL ImF�Km~ELmH.wlF|k?C+L Q<Fh4 Q<F C$; A ~RJQ<R B<F32 A(w ~+k?RoA ~EBxw ~ A ~EBWQWMlFoK B<C+MOQ<F XY Z K(F5w ~ B 0J{fwlF K(F A(B<CqK ImkJQWMlC+L %�. ~EB|Fh4 F32 A(wlF�� wzy MOQ<F32[A → X • Y Z, a1/.../an] MOLmK M1_ ImF=_ ImFxwlF|LmC+L5�zQ<FJB@2 MOL ~Ew A ~ RJQ<R|B<F32 A(w ~+k?R A ~EB XY Z Km~ELmHI(LmF�A(B<C+Q<C+A�:(B�~+H<F5K B<C+MOQ<F5Km~ELmH0w ~/_ ImFJwOwlF A A C+I(N+~EMOQ �JQWB<F�HWI(MONqMlF|A ~EB.I(L K(F?H.H@AB2,( C+wlF?H0Q<FJB@2 My�L ~EI54 a1, ..., an

�(FJQ�_ ImFxKm~ELmH0k?FJQWQ<F|A ~EBWQWMlF|K B<C+MOQ<F��(wzy ~EwO{PC+BWMOQ@:�2 Fo~5B<F?k?C+L(L I I(LmF�H<R _ ImFJLmk?F�K(FH@A!2=( C+wlF?H0k?C+BWB<F?HWA C+LmKm~EL Qv~EI LmC+L5�zQ<FJB@2 MOL ~Ew X

%� k E!�F�5MÌ"�Q�

Fermeture(I)nqC+MOQ I I(L FJLmH<F32,((wlFvK y MOQ<F32 H j r!�fw ~3D FJB@2 FJQWI(B<FvK(F I � LmC+Q<R?F Fermeture(I) � F?HWQ%C/((Q<FJL ImF.A ~EBwlF?H;K(FJI54 B 0J{fwlF?H;HWI(MONf~EL Q<F?H!,$&% psL(MOQWM ~EwlF32 FJL Q�� A(w ~+k?FJB0k : ~/_ ImFxMOQ<F32�K(F I Km~ELmH Fermeture(I)

%�5% n M [A → α • Bβ, a] F?HWQ|Km~ELmH Fermeture(I) FJQ B → γ F?HWQ|I(LmFoA(B<CqK ImkJQWMlC+L K(F G �~EwlC+B<H ~F�WC+I(Q<FJB wzy MOQ<F32 [B → •γ, b]

dFermeture(I) A C+I(B k : ~/_ ImF Q<FJB@2 MOL ~Ew b Km~ELmH

� �� !�βa� �(Hcy MOw LmF3Hcy A QWB<C+I(NPF3A ~+H K(R � d % r.RJA RJQ<FJB wzy ~EA(A(wOMlkc~EQWMlC+L K(Fvk?FJQWQ<F3K(FJI54qM1032 F

B 0J{fwlFb�[ImH _ I y d k?F*_ I y MOw LmF�H<C+MOQ�A(wOImH�A CfH<HWM'((wlFxK y ~F�WC+I(Q<FJB.K y MOQ<F32 H d Fermeture(I)%

� k E!�F�5MÌ"�Q�Transition[I,X]nqC+MOQ I I(L FJLmH<F32=((wlF�K y MOQ<F32 H;FJQ X I(L H@AB2,( C+wlF|K(F G �$&% < ~EwlkJI(wlFJB I ′ �mwzy FJLmH<F32,((wlF K(F?H�MOQ<F32 H [A→ αX • β, a] Q<FJwlH�_ ImF [A→ α •Xβ, a] ∈ I

%�5%

Transition[I,X] = Fermeture(I ′)%

�,�� J "��l&MÌ"�� nH��N�B��P�B��H "��pnJI1IKMP�!��N�� h �,k �QG��GnqC+MOQ G′ = (V ′, T, P ′, S′) w ~ {fB�~�2L2 ~EMOB<F ~EI({&2 FJL Q<R?F5C/((Q<FJL ImF K(F G = (V, T, P, S) FJL ~F�[C+I5�Q�~EL Q wlF0LmC+L5�zQ<FJB@2 MOL ~Ew S′

dV A C+I(B C/((Q<FJL(MOB � yW�Pw ~�A(B<CqK ImkJQWMlC+L S′ → S

dP A C+I(B C/((Q<FJL(MOB P ′

FJQ0FJL B<F32 A(w ~$�c~EL Qvwzy ~F4qMlC/2 F S A ~EB S′ %$&% psL(MOQWM ~EwOMlH<FJB C ~EI H�FJI(w FJLmH<F32,((wlF�K y MOQ<F32 H;LmC+L5� 2 ~EB _ ImR�C/((Q<FJL I A ~EB

Fermeture({[S ′ → •S, $]})%

�5% MP��QM �OGU� MOw�Fh4qMlHWQ<FxK(F?H0FJLmH<F32,((wlF K y MOQ<F32 H;LmC+L5� 2 ~EB _ ImR?H0Km~ELmH C� ��I"�F�

75% nqC+MOQ I I(L FJLmH�F32,((wlF�K y MOQ<F32 H0LmC+L5� 2 ~EB _ ImR K(F C%

]�% k �QG�� k : ~/_ ImF|H@AB2,( C+wlFxK(Fx{fB�~�2L2 ~EMOB<F X ∈ V ∪ T� ��I"�F�

-5% �Ì MOw Fh4qMlHWQ<F3I(L MOQ<F32 [A→ α •Xβ, a] Km~ELmH I�� K��F�

65% n y MOw L y A F?HWQ�A ~+H;K(R � d � ~F�WC+I(Q<FJB Transition[I,X] k?C/2L2 F|FJLmH�F32,((wlFLmC+L5� 2 ~EB _ ImR d C%

ST� %ST� %

�� 65%8W � <�C+LmHWQWBWImkJQWMlC+L K(F?H�Q�~�((wlF?H j r kc~ELmC+L(M1_ ImF?H %

� � <�C+LmHWQWBWImkJQWMlC+L K(F?H0~EL ~Ew'A H<FJI(B<H�A C+I(B;{fB�~�2L2 ~EMOB<F?H;LmC+L5� k?C+L Q<Fh4qQWImFJwOwlF?H

�,��U� MP��GUl&MÌ"�� nU�!�LMP� �� K�!�Nn Iy��U�� O�P� �� l��Q�UI��OGU��Actions

�mMSuccesseursnqC+MOQ G′ I(LmF {fB�~�2L2 ~EMOB<F ~EI({&2 FJL Q<R?F��3wlF?H Q�~�((wlF?H#K y ~EL ~Ew'A H<F j r kc~ELmC+L(M1_ ImF?H Actions FJQ

Successeurs H�C+L Q0C/((Q<FJL ImF?H0A ~EB:,$&% <�C+LmHWQWBWI(MOB<F C = {I0, I1, ..., In}�mw ~ k?C+wOwlF?kJQWMlC+L K(F?H.FJLmH<F32=((wlF?H3K y MOQ<F32 H j r � $�� A C+I(B0w ~

{fB�~�2L2 ~EMOB<F G′%

�5% j y RJQ�~EQ i F?HWQ k?C+LmHWQWBWI(MOQ d A ~EBWQWMOB�K(F.wzy FJLmH<F32,((wlFxK y MOQ<F32 H Ii% j F?H�~+kJQWMlC+LmH�K y ~EL ~Ew'AqH<F.A C+I(B

wzy RJQ�~EQ i H�C+L Q0K(RJQ<FJB@2 MOLmR?F?H.A ~EB�wlF?H�B 0J{fwlF?H0H<I(MON+~EL Q<F?H!,� ~ � n M [A → α • aβ, b] ∈ Ii

~?NPF?k a ∈ T FJQ HWM Transition[Ii, a] = Ij�0~EwlC+B<H

Action[i, a] = �6R(<72$)W*�� j %� ( � n M [A→ α•, a] ∈ Ii

� A 6= S′ Action[i, a] = �PR�� T �(* par A→ α%

� k � n M [S′ → S•, $] ∈ Ii�m~EwlC+B<H Action[i, $] = accepter

%n M wlF?H B 0J{fwlF?H A(B<R?k?R?K(FJL Q<F?H.H<C+L Q�k?C+LHOmMlkJQWImFJwOwlF?H�� ~EwlC+B<H w ~ {fB�~�2L2 ~EMOB<F3L y F?HWQ A ~+H j r � $�� FJQwzy ~EwO{PC+BWMOQ@:�2 F5R?k :mC+ImF %

75% n M A ∈ V FJQ Transition[Ii, A] = Ij~EwlC+B<H Successeurs[i, A] = j

%]�% a C+I(Q<F?H wlF?H FJL QWB<R?F?H LmC+L5� K(Rh\mL(MlF?H A ~EB wlF?H B 0J{fwlF?H FJL � � � FJQ � 7 � H<C+L Q A CfHWMOQWMlC+L(LmR?F?H d

* � �(* �� %-5% j y RJQ�~EQ MOL(MOQWM ~Ew0K(F wzy ~EL ~Ew'AqH�FJI(B F?HWQ k?FJwOI(M�_ I(M0~ RJQ<R k?C+LmHWQWBWI(MOQ d A ~EBWQWMOB K(F wzy FJLmH<F32,((wlFk?C+L Q<FJL ~EL Q.wzy MOQ<F32 [S′ → •S, $]

%

�� 65%'$PZ � <�C+LmH<QWBWImkJQWMlC+L K(F?H�Q�~�((wlF?H j r kc~ELmC+L(M1_ ImF?H � HWI(MOQ<F �h%

�,��U� MP��GUl&MÌ"�� nU�!�LMP� �� K�!�Nn Iy��U�� O�P� �>j��Actions

��MSuccesseurst L ~EwO{PC+BWMOQ@:�2 F DG~+kJMOwlF��O2 ~EMlH|{PC+I(B@2 ~ELmK�FJL�A(w ~+k?F k?C+LmHWMlHWQ<F d k?C+LmHWQWBWI(MOB<F K y ~�( C+B<K#wlF?H|MOQ<F32 Hj r � $�� A(I(MlH d D ImHWMlC+L(LmFJB�wlF?H;FJLmH�F32,((wlF?H;K y MOQ<F32 H.K(F�2��32 F3LmCPA ~EI � FJLmH<F32=((wlF?H0K y MOQ<F32 H0MlK(FJL5�

QWM1_ ImF?H��m~EI54 H@AB2,( C+wlF?H;K(F3A(B<RJNqMlHWMlC+L A(B 0?H �h%$&% <�C+LmHWQWBWI(MOB<F C = {I0, I1, ..., In}

�mw ~ k?C+wOwlF?kJQWMlC+L K(F?H.FJLmH<F32=((wlF?H3K y MOQ<F32 H j r � $�� A C+I(B0w ~{fB�~�2L2 ~EMOB<F G′

%�5% . C+I(B5k;: ~/_ ImF LmCPA ~EI�A(B<R?H�FJL Q�A ~EB@2 M�wlF?H|FJLmH<F32=((wlF?H K y MOQ<F32 H j r � $�� QWB<C+I(NPFJB�Q<C+ImH|wlF?HRJQ�~EQ<H.~PA ~EL Qvk?F+2��32 FxLmCPA ~EI FJQ;B<F32 A(w ~+k?FJB.k?F?H;RJQ�~EQ<H;A ~EB;wlFJI(B;I(L(MlC+L %

75% nqC+MOQ C ′ = {J0, J1, ..., Jn}��w ~ k?C+wOwlF?kJQWMlC+L K(F?H FJLmH<F32=((wlF?H K y MOQ<F32 H j r � $�� B<R?HWI(wOQ�~EL Q<F %. C+I(B�k : ~+kJI(L K(F�k?FJI54!� kJM �PK(RJQ<FJB@2 MOLmFJB%wlF?H%~+kJQWMlC+LmH�K y ~EL ~Ew'A H<F�k?C/2L2 F;Km~ELmH�wzy ~EwO{PC+BWMOQ@:�2 F

A C+I(B k?C+LmHWQWBWI(MOB<F wlF?H Q�~�((wlF?H j r�kc~ELmC+L(M1_ ImF?H % n M0k?F?H B 0J{fwlF?HN2N0JLmFJL Q d I(L k?C+LHOmMOQ��w ~{fB�~�2L2 ~EMOB<F|L y F?H<Q;A ~+H j [ j r � $�� FJQ�wzy ~EwO{PC+BWMOQ@:�2 F R?k;:mC+ImF %

]�% j ~ DGC+LmkJQWMlC+L Transition F?HWQ#k?C+LmHWQWBWI(MOQ<F k?C/2L2 F HWI(MOQ % nqC+MOQ J = I0 ∪ I1 ∪ ... ∪Ik��wlF?H5LmCÀ ~EI54 K(F Transition[I0, X] � Transition[I1, X] � %'%'% FJQ Transition[Ik, X]H<C+L Q'wlF?H 2��32 F?H A(I(MlH _ ImF I0, I1, ..., Ik

C+L Q'wlF 2��32 F LmCPA ~EI % nqC+MOQ K wzy I(L(MlC+L K(FQ<C+ImH wlF?H FJLmH<F32=((wlF?H K y MOQ<F32 H ~ A ~EL Q wlF 2��32 F LmCÀ ~EI _ ImF Transition[I0, X]

% [ wlC+B<HTransition[J,X] = K

%-5% j ~ Q�~�((wlF Successeur F?H<Q3k?C+LmH<QWBWI(MOQ<F k?C/2L2 F A C+I(Bxk?FJwOwlF K(F?H3Q�~�((wlF?H j r kc~ELmC+L(M1_ ImF?H��2 ~EMlH0H<I(B�w ~ k?C+wOwlF?kJQWMlC+L K y FJLmH<F32=((wlF?H.K y MOQ<F32 H C ′ %

�� 65%'$&$ � <�C+LmHWQWBWImkJQWMlC+L K(F?H;Q�~�((wlF?H j [ j r %

� ��

� �� !�"��#$�� %�� &� �"��')(�� (��

*,+.-0/21436587:9;7=<6+.5?>@9;AB9;5 A 10+C<D> 36AE+.F : -:9G10+H+2147I36AE+C<6/J-4K8LG9;74KNMGAPOQ36KRFS+J367=9;5870+J-4AB9;74K8LT+JUP+JAQ7WVJ74-0+.-0+JF6-0/YX10+JAQ70/2+ZFB9;-)36A[9;-4\6-0+]<6+Z<6/J-4K8L^9;74KNMGA,_B*`>@9;-4\6-0+a<6+Z<6/J-4K8L^9;74KNMGA[+YbRF658KNcJK870+Z5d9e1474-43EcJ7436-0+a<6+f5d9gF : -:9G10+]+JA70+J-4UP+h<6+H-0+JUgF65d9Gc2+JUP+JAi701H143Ec2c2+21:14Kkjl1W<6+21ÀEMGARX?70+J-4UgK8AB9;3RbmFB9;-W<6+21.10/2Oi3E+JAEc2+21.<6+)70+J-4UgK8AB9;3Rbn+J7WAEMGARX70+J-4UgK8AB9;3RbDoqp]5d9fj?9Gr2MGAm<6+s5?>@9;AB9;5 A 10+s<6+21`5d9;A6ti9;tT+21WAB9;7436-0+J5N1Zuvjw-:9;AErx9;KN1yoiFB9;-.+YbR+JUgF65N+yz`MG{n36AE+|F : -:9G10+10+ec2MGUgF}M^10+g<D> 36A~143G�4+J7xoS<D> 36A�LT+J-4\}+g+J7Z<D> 36A~c2MGUgF65N/JUP+JAi7xo�+J70c^_D*=>@9;AB9;5 A 1:+eUPMGAi74-0+POQ3E+e5d9mF : -:9G10+j?9;K87s\6KN+JA!FB9;-474KN+�<R3!5d9;A6ti9;tT+e+JA6tT+JAE<R-0/�FB9;-s5d9nt^-:9;UgUn9;K8-0+^_}��FB9;-474K8-f<6+�5dpRoSMGA[F}+J367s1x> K8AQ70/J-0+21010+J-]p<D>@9;3674-0+21HF6-0MGF6-4KN/J70/21|t^-:9;UgUn9;74KNcx9;5N+21x_E�Z9;AE1C5N+Z<6MGUn9;K8AE+Z<6+21C5d9;A6ti9;tT+21|<6+hF6-0MGt^-:9;UgUn9;74KNMGA,oBMGA�F}+J3671x> K8AQ70/J-0+21010+J-�p�5d9�c2MGAEc2MG-0<E9;AEc2+�<6+21]7 A F}+21�FB9;-�+Yb6+JUgF65N+^_ < +PtT+JA6-0+�<6+PLT/J-4Kk�Bcx9;74KNMGAE1e<6+nF6-0MGF6-4KN/J70/21t^-:9;UgUn9;74KNcx9;5N+21h10MGAi7)-0/x9;58KN1:/2+21)FB9;-)c2+]OQ3E+f5?>�MGA[9;F6F}+J585N+]<6+21a�G��^��;�2�Y�h�x�Y�P�G�B�l��J�E��m��E d¡,¢y£[¢x¤q¥~�E�S¦y§w¨,©�£~ª cx9;5NcJ365�<6+fF6-0MGF6-4KN/J70/21h1436-H36A[9;-4\6-0+]<6+Z<6/J-4K8L^9;74KNMGA

�h+.UPVJUP+ôTMGAeF}+J367�74-:9;AE1«jlMG-4UP+J-�5d9hF : -:9G1:+H+JA�36AE+)9;3674-0+CF : -:9G1:+ô^/JLT+JAi743E+J585N+JUP+JAi7.<E9;AE1�36AP9;3674-0+5d9;A6ti9;tT+ôQFB9;-`74-:9G<R3EcJ74KNMGA�MG3mc2MGUgF6K85d9;74KNMGA,_q*,+21.9;AB9;5 A 10+21W10/JUn9;Ai74KNOQ3E+21C+J7`5N+21=74-:9G<R3EcJ74KNMGAE1.FB9;-47:9;tT+JAQ736AE+s9;F6F6-0Mqc : +sc2MGUgUa36AE+fOQ36KBc2MGAE14KN1470+hpZVJ74-0+|<6/Y�EA6KN+21WFB9;-=K8AE<R3EcJ74KNMGA�1436-=5d9]1074-43EcJ7436-0+|<6+)5d9ZF : -:9G10+ô<6MGAEcZ1436-C5d9�j�MG-4UP+h<6+f5?>@9;-4\6-0+Z<6+Z<6/J-4K8L^9;74KNMGA,_6¬sA�<6+21Hcx9G<R-0+21)7 : /2MG-4KNOi3E+21)OQ36K,9e/J70/f<6/JLT+J5NMGF6FS/ZF}MG36-<6/Y�EA6K8-H<6+21.9;AB9;5 A 10+hMG3�<6+21W74-:9;AE1«j�MG-4Un9;74KNMGAE1CFB9;-WK8AE<R3EcJ74KNMGA�1436-.5d9�1474-43EcJ7436-0+s<6+21.F : -:9G10+21.1x>@9;F6F}+J585N+5N+21|G®4�G�e�P�G�w®4��T��l®��?¯Y�E�0��°±�E¥�¥~�E§w°;£n�R¦2¦x°G§v²�©�¤i£[ª t^-:9;UgUn9;K8-0+|AEMGARX³c2MGAQ70+Ybq743E+J585N+hF}MG36-`5d9GOQ3E+J585N+|MGAm9G101:MQcJKN+H36AMG3�<6+21Z9;7474-4K8\636701Z9;3Rb[1 A Ua\}MG5N+21h+J7hMG{�pmc : 9GOQ3E+�-0´Jt^5N+�<6+�F6-0Mq<R3EcJ74KNMGA�MGA�9G1010MqcJKN+]36AE+MG3µF6583E14KN+J36-01m-0´Jt^5N+21m<6+[cx9;5NcJ365sF}+J-4UP+J747:9;Ai7�<6+¶cx9;5NcJ365N+J-�5d9�L^9;5N+J36-m<6+21�9;7474-4K8\636701�<6+211 A U�\SMG5N+21 A 9;F6FB9;-:9;KN101:9;AQ7x_

*,+21It^-:9;UgUn9;K8-0+21=9;7474-4K8\63E/2+21�10MGAi7I5d9;-4tT+JUP+JAi7�3674K858KN10/2+21�+JAec2MGUgF6K85d9;74KNMGAP<6+21�5d9;A6ti9;tT+21�<6+`F6-0MGt^-:9;UeXUn9;74KNMGA,oxUn9;KN1�F6583E1�tT/JAE/J-:9;5N+JUP+JAQ7I+J585N+21IMGAi7I<6+�AEMGUa\6-0+J3E1:+21I9;F6F658KNcx9;74KNMGAE1IF6-:9;74KNOQ3E+21�<E9;AE1�5?> K8AE<R3E1474-4KN+^_�Z9;AE1)c2+Zc : 9;F6K874-0+ôBAEMG3E1|9;585NMGAE1HLTMGK8-|<6+J3Rb�-0/x9;58KN1:9;74KNMGAE1s<6+ft^-:9;UgUn9;K8-0+21s9;7474-4K8\63E/2+21a�R5N+21|<6/Y�EA6K874KNMGAE1<RK8-4K8tT/2+21)FB9;-|5d9e1 A AQ7:9±bR+a+J7H5N+21)10c : /JUn9G1s<6+Z74-:9G<R3EcJ74KNMGA,_·h¸�¹ º¼»�½e¾�¿«ÀS¿ � ¾�ÁÃÂ�¿4ÄS¿:Å)»�Æ�ÁÈÇeÉHÄ%Ê0É�ÁBËZ¾|ÀSÉCÌ]ÆÍ³5�+YbRKN1470+e<6+J3Rb[t^-:9;AE<61Z7ÏÎQF}+21Z<D>@9;7474-4K8\636701]<E9;AE1f5N+21ft^-:9;UgUn9;K8-0+21�9;7474-4K8\63E/2+21n��5N+21P�T��l®��?¯Y�R�w��Y�;�BÐ�wÑR�J�l�v�2�Y�a+J7)5N+21a�^��l®Y��¯J�q�w�fÑR�Y®Y�l�³��Y_

�� AB9;58ÎR10+Z10/JUn9;AQ74KNOi3E+ôEt^-:9;UgUn9;K8-0+21h9;7474-4K8\63E/2+21s+J7)74-:9;AE1«j�MG-4Un9;74KNMGAE1��¦2¦x°G§w²I©�¦¶¢2¡��S¦��¤T¦y§w¢x¤µª 9;7474-4K8\6367a<D> 36A"14ÎqUa\}MG5N+eAEMGARX?70+J-4UgK8AB9;5W+JA"FB9;-474KN+gti9;3Ec��E+P<6+-0´Jt^5N+m<6+gF6-0Mq<R3EcJ74KNMGA�<6MGAi7�5d9�L^9;5N+J36-a+2147acx9;5NcJ365N/2+�p�FB9;-474K8-�<6+21aLG9;5N+J36-01�<6+21�9;7474-4K8\636701<6+21|14ÎQU�\SMG5N+21h9;F6FB9;-:9;KN101:9;AQ7|+JA�FB9;-474KN+]<R-0MGK870+]<6+a10+21H-0´Jt^5N+21)<6+ZF6-0Mq<R3EcJ74KNMGA,_��¦2¦x°G§w²I©�¦��¤Q°;§v¦x¤�ª 9;7474-4K8\6367=<D> 36AP14ÎqUa\}MG5N+CAEMGARX?70+J-4UgK8AB9;5�+JAgFB9;-474KN+H<R-0MGK870+)<D> 36AE+C-0´Jt^5N+<6+=F6-0MQ<R3EcJ74KNMGA�<6MGAi7,5d9CL^9;5N+J36-�+2147,cx9;5NcJ365N/2+.p.FB9;-474K8-�<6+21,L^9;5N+J36-01,<6+21�9;7474-4K8\636701I<6+21�9;3674-0+2110ÎQU�\SMG5N+21)<6+]5d9�-0´Jt^5N+]<6+ZF6-0Mq<R3EcJ74KNMGA�uwÎ�c2MGUgF6-4KN1H5N+]14ÎqUa\}MG5N+Z+JA�FB9;-474KN+Zti9;3Ec�E+yzY_

�583E1�+YbqF658KNcJK870+JUP+JAQ7xofFSMG36-[36AE+"F6-0Mq<R3EcJ74KNMGAA → X1X2...Xn

o)36AE+�-0´Jt^5N+�10/JUn9;AQ74KNOi3E+b =

f(c1, ..., ck)FS+J367ecx9;5NcJ365N+J-e36A 9;7474-4K8\6367g14ÎqAi7��E/J74KN1:/

b<R3�AEMGARX?70+J-4UgK8AB9;5

Ap¶FB9;-474K8-�<6+21g9;7474-4K8\636701

c1, ..., ck

<6+21.14ÎQU�\SMG5N+21X1, ..., Xn

oQMG3�+JAEc2MG-0+hcx9;5NcJ365N+J-.5d9aL^9;5N+J36-.<D> 36A�9;7474-4K8\6367��E/J-4K870/b<D> 36A�14ÎqUeX\}MG5N+

Xi

p�FB9;-474K8-s<6+21s9;7474-4K8\636701c1, ...ck

<6+21)14ÎqUa\}MG5N+21A,X1, ...Xn

_

�� £Q¥�� w£�� MGK87)5d9�t^-:9;UgUn9;K8-0+n�L → E �E → E � T | T

T → T � F | F

F → ( E - | n

MG{n+2147|36A¶AEMGUa\6-0+�+JAi74KN+J-x_��sA�F}+J367s/2cJ-4K8-0+a36AE+a<6/Y�EA6K874KNMGA[<RK8-4K8tT/2+�FB9;-)5d9n14ÎQAQ7:9±bR+]FSMG36-hcx9;5NcJ365N+J-5d9�L^9;5N+J36-|<D> 36A[9;7474-4K8\6367 �"!$#g-0+JF6-0/210+JAi7:9;AQ7|5d9eL^9;5N+J36-|<6+f5?>�+YbRF6-0+21014KNMGA¶<6+f5d9eUn9;A6KN´J-0+a1436K8LG9;AQ70+P�

�-0Mq<R3EcJ74KNMGA %|´Jt^5N+Z10/JUn9;AQ74KNOi3E+F → n F & �'!(#*) �,+-& �'!$#(#$.0/F → ( E - F & �'!(#*) � E & �"!$#T → F T & �'!(#*) � F & �"!$#T → T1 � F T & �"!$#*) � T1 & �'!(# ×F & �'!(#E → T E & �"!$#*) � T & �"!$#E → E1 � T E & �"!$#*) � E1 & �"!$# +T & �'!(#L→ E � 13254(68792 . 6 ( E & �'!(# -

MG{�5?>@9;7474-4K8\6367 �"!$#(#$.:/�+2147H36A[9;7474-4K8\6367|cx9;5NcJ365N/]5NMG-01|<6+f5d9e-0+2c2MGA6AB9;KN101�9;AEc2+]<R3�70+J-4UgK8AB9;5nuw7³ÎqF6KNOQ3E+YXUP+JAi7|5NMG-01|<6+f5?>@9;AB9;58ÎR10+Z5N+YbRKNc2MGt^-:9;F"�6KNOi3E+�<E9;AE1H36A�5d9;A6ti9;tT+]<6+ZF6-0MGt^-:9;UgUn9;74KNMGA�zY_

2

*,+21]9;7474-4K8\636701Z14ÎqAi7��E/J74KN10/21fF}M^1010´2<6+JAQ7h36AE+�F6-0MGF6-4KN/J70/e74-0´21hK8UgF}MG-47:9;Ai70+P+JA�c2+eOi36K�c2MGAEc2+J-4AE+e5N+J36-MG-0<R-0+�<D>�/JL^9;583B9;74KNMGA <E9;AE1g36A 9;-4\6-0+�<6+�<6/J-4K8L^9;74KNMGA,_<;�A +>=D+J7xoIc2MGUgUP+�5?>@9;7474-4K8\6367n<6+�c��B9GOQ3E+�AEMGARX70+J-4UgK8AB9;5�FS+J367fVJ74-0+ecx9;5NcJ365N/gpPFB9;-474K8-f<6+21hLG9;5N+J36-01f<D>@9;7474-4K8\636701Z<6+�10+21s�E5N1xoBK85�+2147sFSM^1010K8\65N+�<D>�/JL^9;583E+J-70MG3E1�5N+21�9;7474-4K8\636701e14ÎqAi7��E/J74KN10/21e+JA�FB9;-0c2MG36-:9;Ai7e5?>@9;-4\6-0+m<6+JF636KN1�5N+21ajl+J36K8585N+21|�«3E10Oi3,>@p�5d9�-:9GcJK8AE+^_@?.+J7MG-0<R-0+�+2147�+Yb69GcJ70+JUP+JAQ7�c2+J5836KhOQ3E+[1036K87m5?>@9;AB9;58ÎR10+�9G10c2+JAE<E9;Ai70+�<6+!7³ÎqF}+[*A%�_WÍÏ5f+2147m<6MGAEc!F}M^1014K8\65N+<D>�/JL^9;583E+J-)c2+21)9;7474-4K8\636701sp�5d9�LTMG5N/2+ô6c^>�+2147«XÏp±X³<RK8-0+fF}+JAE<E9;Ai7)5d9�cJ-0/x9;74KNMGA¶<6+f5?>@9;-4\6-0+Z<6+f<6/J-4K8L^9;74KNMGA�5NMG-01<6+Z5?>@9;AB9;58ÎR10+^_

�� £Q¥�� w£��CB �MG36-Z5d9mt^-:9;UgUn9;K8-0+P9;7474-4K8\63E/2+eF6-0/2c2/2<6+JAQ70+ô,cx9;5NcJ365NMGAE1Z5N+21Z9;7474-4K8\636701]1436-f5d9nF"�6-:9G10+D �(E"�GF0� �

�q_��]�f/Y�EA6K874KNMGAE1|<RK8-4K8tT/2+21|FB9;-)5d9e14ÎqAi7:9±b6+ ��

� & 13254$6 792 . 6 (�� D - *

}}}}

}}}}

}}}}

}}}}

}}}}

RRRRRRRRRRRRRRRRRRRR

�

;

rrrrrrrrrrrrr

UUUUUUUUUUUUUUUUUUUUUUUUUU � & ; & �'!$#*) � � D &� & �'!(# ) � � �

D & ; & �'!(# ) � D ; �

yyyy

yyyy

y

EEEEE

EEEE

� &�� & �'!(#*) ��F

� &� & �"!$#*) � D F@&� & �'!(# ) � E � �

� &�� & �'!$#*) � D � E-&�� & �'!$# ) � E � c��6K =}-0+ô F ∗c�6K =S-0+ô D c��6K =}-0+ô E

*,+21HAQ36UP/J-0M^1s+JA[/J74KNOi3E+J7470+21HK8AE<RKNOQ3E+JAi7s5?>�MG-0<R-0+ZFB9;-)5N+2OQ3E+J5,5N+21|9;7474-4K8\636701s10MGAi7|cx9;5NcJ365N/21y_2

*,+21H9;7474-4K8\636701H14ÎQAQ7��E/J74KN10/21C10MGAi7.5N+21WF6583E1.10K8UgF65N+21Cp�c2MGUgF6-0+JAE<R-0+f+J7Cp�cx9;5NcJ365N+J-x_RÍ³5}10MGAQ7W\}+x9;3Ec2MG36F3674K858KN10/21�<E9;AE1,70MG3670+21�5N+21,<6/Y�EA6K874KNMGAE1�<6+�74-:9;AE1«j�MG-4Un9;74KNMGAE1�OQ36KTF}+J36LT+JAi7�1y>@9;F6FB9;-0+JAi70+J-�pH<6+�5?>�/JL^9;583B9;74KNMGA9;3a10+JAE1�5d9;-4tT+^_y*,+21I9;7474-4K8\636701 �E/J-4K870/21yoxFB9;-�c2MGAQ74-0+ôyMGAQ7�36AE+=t^-:9;AE<6+`K8UgFSMG-47:9;AEc2+`FSMG36-�UPMQ<6/J58KN10+J-�70MG3670+F6-0MGF6-4KN/J70/gMG{�K85�Î!9�<6/JFS+JAE<E9;AEc2+g+JAQLT+J-01Z5N+ec2MGAi70+YbR70+^_ ?h>�+2147f5N+ecx9G1fFB9;-f+Yb6+JUgF65N+g<6+�5?>�MG\658K8ti9;74KNMGA�p<6/2cJ5d9;-0+J-�36AE+¶L^9;-4Kd9;\65N+�92L^9;Ai7�<6+¶5?> 3674K858KN1:+J-�MG3 5N+�7ÏÎQFB9;tT+�<6+21�+YbqF6-0+21:14KNMGAE1�<E9;AE1m5N+21m5d9;A6ti9;tT+21�<6+F6-0MGt^-:9;UgUn9;74KNMGA,_ �� £Q¥�� w£�� ?.+J7Z+YbR+JUgF65N+�K858583E1474-0+e5?> 3674K858KN1:9;74KNMGA~<D>@9;7474-4K8\636701��E/J-4K870/21fFSMG36-f74-:9;K870+J-]<6+21f-0´Jt^5N+21Z<6+7³ÎqFB9;tT+]<E9;AE1|36A�5d9;A6ti9;tT+a<6+fF6-0MGt^-:9;UgUn9;74KNMGA,_ � MGK87)5d9�t^-:9;UgUn9;K8-0+n�

D → T L

T →. +��87 . 6 | 6�� .(#

L → L �>7�� | 7��MG{a36AE+W<6/2cJ5d9;-:9;74KNMGA��&+2147�jlMG-4UP/2+W<D> 36AaAEMGU�<6+=7ÏÎQF}+��+J7�<D> 36AE+`58KN1470+`<D> KN<6+JAQ74Kk�Bcx9;70+J36-01�<6+=L^9;-4Kd9;\65N+21��_6*�9et^-:9;UgUn9;K8-0+�9;7474-4K8\63E/2+]1036K8LG9;AQ70+]/JLG9;583E+a<6+21|9;7474-4K8\636701 � �$4 .g+J7 ��(4 .�!!uwF}MG36-)7³ÎqFS+ �E/J-4K870/yzZ�

�-0Mq<R3EcJ74KNMGA %|´Jt^5N+]10/JUn9;AQ74KNOi3E+D → T L L &"��(4 .#! ) � T &$��(4 .T →

. +��87 . 6 T &"��(4 .*) � . + �87 . 6T → 6%� .$# T &"��(4 .*) �,6�� .$#L→ L1 � 7&� L1 &$� �$4 .#! ) � L &"��$4 .#!+J7 ! ')(#* � . 6 +��$4 . ( 7�� & . + �$6 .(. � L &$� �$4 .#! -L→ 7&� !�' (�* � . 6�+ �$4 . ( 7&� & . +��(6 .$. � L &$� �$4 .�! -

MG{!5d9nF6-0Mqc2/2<R36-0+ ! ')(#* � . 6 +��$4 .mLG9P-0+JAE10+JK8tÂE+J-Z5N+�c��B9;UgF�7³ÎqFS+g9G101:MQcJKN/2+epP5?>�+JAQ74-0/2+e<6+�5d9n7:9;\65N+e<6+2114ÎqUa\}MG5N+21Pc2MG-4-0+214F}MGAE<E9;Ai7�p!5d9�LG9;-4Kd9;\65N+^_`�f9;AE1P36A c2MGUgF6K85d9;70+J36-xo=5d9!7:9;\65N+�<6+21n14ÎQU�\SMG5N+21n+2147g36AE+

�� AB9;58ÎR10+Z10/JUn9;AQ74KNOi3E+ôEt^-:9;UgUn9;K8-0+21h9;7474-4K8\63E/2+21s+J7)74-:9;AE1«j�MG-4Un9;74KNMGAE11474-43EcJ7436-0+e<6+�<6MGA6AE/2+21sF6-4K8UPMG-0<RKd9;5N+gOQ36K�c2+JAi74-:9;58KN10+�70MG3670+21h5N+21hK8ARjlMG-4Un9;74KNMGAE1f-0+J5d9;74K8LT+21Z9;3Rb¶KN<6+JAQ74Kk�6Xcx9;70+J36-01|OQ36K,10MGAQ7)AE/2c2+2101:9;K8-0+21HF}MG36-)5d9�74-:9G<R3EcJ74KNMGA[LT+J-01)5N+f5d9;A6ti9;tT+]Un9Gc�6K8AE+^_?.MGAE14KN<6/J-0MGAE1�Un9;K8Ai70+JAB9;AQ7`5?>�/JL^9;583B9;74KNMGAe<6+21=9;7474-4K8\636701 � �$4 .h+J7 � �$4 .#!ZF}MG36-�5d9sF"�6-:9G10+f> 6�� .$# 7�� 1 �

7�� 2 � 7&� 3

>8_

� &� &$��(4 .*) �,6%� .$# D

kkkkkkkkkkkkkkkkkkkkkkkkk

TTTTTTTTTTTTTTTTTTTTTTTTTTTTT

� & * &"��(4 .#! ) � 6%� .(#D & ! ' (�* � . 6�+ �$4 . ( D � 6�� .(# -

TE & * &$� �$4 .#! ) �,6�� .$#

F@& !�' (#* � . 6�+��(4 . ( � � 6%� .$# - L

ssssssssssssss

LLLLLLLLLLLLLL

6 .$.$# L

ssssssssssssss

KKKKKKKKKKKKK� 7&� 3

� & * &$� �$4 .#! ) �,6�� .$# & !�' (#* � . 6�+��(4 . ( � � 6�� .$# - L � 7&� 2

7�� 1

;�AEc2MG-0+�c2+J7470+njlMGKN1xo,5N+21�AQ36UP/J-0M^1e+JA�/J74KNOQ3E+J7470+21�K8AE<RKNOi3E+JAQ7�5?>�MG-0<R-0+�10+J5NMGA�5N+2Oi3E+J5.5N+21�9;7474-4K8\636701e10MGAQ7cx9;5NcJ365N/21x_2

�� !"��#��$��%&�'��!

(sMG3E1)9xLTMGAE1HLQ3�OQ3E+h5?>�MG-0<R-0+Z<D>�/JLG9;583B9;74KNMGA�5N+fF6583E1H14K8UgF65N+hF}MG36-C5N+21)9;7474-4K8\636701)+2147Hc2+J5836K,<6+21)9;7474-4KkX\636701C14ÎqAi7��E/J74KN10/21x_qÍÏ5�143*)P7.<D>�/JLG9;583E+J-C5N+21C9;7474-4K8\636701H+JAnFB9;-47:9;Ai7)<6+21`j�+J36K8585N+21.<6+|5?>@9;-4\6-0+f<6+s<6/J-4K8L^9;74KNMGA+JA�-0+JUPMGAQ7:9;Ai7fLT+J-01)5d9e-:9GcJK8AE+^_�(sMG3E1h92LTMGAE1h/Jti9;5N+JUP+JAi7sj�9;K87|-0+JUn9;-0Oi3E+J-hOi3E+]c2+J7hMG-0<R-0+]<D>�/JL^9;583B9;74KNMGAc2MG-4-0+214F}MGAE< FB9;-«j?9;K870+JUP+JAi7�p�5?>�MG-0<R-0+[<6+¶cJ-0/x9;74KNMGA <6+21PA,+f3E<61�<6+�5?>@9;-4\6-0+!<6+¶<6/J-4K8L^9;74KNMGAµ<E9;AE1m5N+219;AB9;58ÎR10+21|9G10c2+JAE<E9;AQ70+21s<6+f7ÏÎQF}+]*A%�_�°±�E¥�¥~�E§w°;£.-0/:�R¦2¦x°;§w²�©�¤Q£"ª 36AE+]t^-:9;UgUn9;K8-0+ � XÏ9;7474-4K8\63E/2+e+2147)36AE+at^-:9;UgUn9;K8-0+�9;7474-4KkX\63E/2+a<6MGAi7|70MG3E1)5N+21|9;7474-4K8\636701|10MGAQ7|14ÎqAi7��E/J74KN10/21y_

1 -:9;UgUn9;K8-0+21 � XÏ9;7474-4K8\63E/2+21�+J7�9;AB9;58Îq1:+[9G10c2+JAE<E9;AQ70+[*A%�j�MG-4UP+JAi7�36Aµc2MG36F65N+!<D>�MG3674K85N1nKN<6/x9;5f+JA70+J-4UP+|<D>�+2)ncx9GcJK870/ôiF636KN10OQ3E+H5?>�/JLG9;583B9;74KNMGA�<6+21`9;7474-4K8\636701.10+Cj?9;K87`pf5d9fLTMG5N/2+h9;3nc2MG36-01`<6+H5d9ZtT/JAE/J-:9;74KNMGA<6+s5?>@9;-4\6-0+^_5;=Anj?9;K87xoTK85SA,>�+2147.UPVJUP+|FB9G1.AE/2c2+2101:9;K8-0+h<6+hcJ-0/2+J-W5?>@9;-4\6-0+f<6+h<6/J-4K8LG9;74KNMGA�FSMG36-Ccx9;5NcJ365N+J-C5N+219;7474-4K8\636701|10ÎQAQ7��E/J74KN10/21x_�f9;AE1�5N+�cx9G1�tT/JAE/J-:9;5?oC5?>�MG-0<R-0+�<D>�/JL^9;583B9;74KNMGA&AE/2c2+2101:9;K8-0+!F}MG36-�5N+21�9;7474-4K8\636701�FS+J367�VJ74-0+�70MG7:9;5N+YXUP+JAi7�<RK =D/J-0+JAi7�<6+¶c2+J5836Ks<6+¶5d9�cJ-0/x9;74KNMGA <6+21nA,+f3E<61�<6+�5?>@9;-4\6-0+[<6+¶<6/J-4K8L^9;74KNMGA,_-;�A j�9;K87xoWc��B9GOQ3E+-0´Jt^5N+P10/JUn9;AQ74KNOi3E+n/J7:9;\658K87�<6+21]<6/JF}+JAE<E9;AEc2+21a+JAQ74-0+P5N+21ZL^9;5N+J36-01]<D>@9;7474-4K8\636701x_�*�9�UP/J7��EMq<6+gtT/JAE/J-:9;5N+F}MG36-g5?>�/JLG9;583B9;74KNMGA <6+21P9;7474-4K8\636701m<D> 36AE+�t^-:9;UgUn9;K8-0+[9;7474-4K8\63E/2+�c2MGAE10KN1470+�<6MGAEc�p�cJ-0/2+J-g36A t^-:9;F"�E+MG{�5N+21�A,+f3E<61g1:MGAi7e5N+21�LG9;5N+J36-01e<D>@9;7474-4K8\636701np[cx9;5NcJ365N+J-g+J7�5N+21g9;-0c21�-0+JF6-0/210+JAQ70+JAi7P5N+21�-0+J5d9;74KNMGAE1g<6+<6/JF}+JAE<E9;AEc2+21s+JAQ74-0+�c2+21|LG9;5N+J36-01x_ � K�5N+Zt^-:9;F"�E+�MG\670+JAi3!+2147s1�9;AE1|cJÎRcJ5N+ôEMGA¶F}+J367s<6/J70+J-4UgK8AE+J-h5?>�MG-0<R-0+<D>�/JL^9;583B9;74KNMGA�+JA�9;F6F658KNOQ3B9;Ai7C36A�9;58tTMG-4K87��6UP+Z<RK87C<6+��l®��I��354*3G�630G��J�E�JoEc^>�+2147«XÏp±X³<RK8-0+h36A�9;58tTMG-4K87��6UP+hOQ36KF6-0Mq<R36K87)36AE+]10/2OQ3E+JAEc2+87;cJ-0MGKN101:9;AQ70+:9�<6+ZA,+f3E<61)1036K8LG9;AQ7)5?>�MG-0<R-0+a<6+Z<6/JF}+JAE<E9;AEc2+^_

�q_�� c�E/JUn9P<6+f74-:9G<R3EcJ74KNMGA � �

� KI5N+�t^-:9;F"�E+P<6+e<6/JF}+JAE<E9;AEc2+gc2MGAi74KN+JAQ7]36A~cJÎqcJ5N+ôD9;5NMG-01f5N+ecx9;5NcJ365=<6+21]9;7474-4K8\636701fj?9;K87]9;F6FB9;-:9��N74-0+36AE+Z<6/JF}+JAE<E9;AEc2+]cJK8-0cJ365d9;K8-0+]<D> 36AE+fL^9;5N+J36-)<D>@9;7474-4K8\6367|+JAiLT+J-01)+J585N+YX?UPVJUP+^_B�f9;AE1|c2+J-47:9;K8AE1)<6+Zc2+21Hcx9G1xoK85E+2147�F}M^1014K8\65N+H<D>@9;F6F658KNOQ3E+J-`36AE+H70+2c�6A6KNOi3E+|<RK870+)<6+ 4*3G�w�B��i�sMG{PMGAn<6MGA6AE+H36AE+HL^9;5N+J36-�K8A6K874Kd9;5N+)F}MG36-36A~c2+J-47:9;K8A~A,+f3E<~<E9;AE1]5N+et^-:9;F"�E+P<6+g<6/JFS+JAE<E9;AEc2+ô,F636KN1]MGA~cx9;5NcJ365N+g-0/JF}/J74K874K8LT+JUP+JAi7a5N+21�9;7474-4K8\636701�«3E10Oi3,>@p�c2+nOi3E+e5N+21ZL^9;5N+J36-01aMG\670+JAQ3E+21]AE+Pc�B9;A6tT+JAi7�F6583E1�DMGA�9�9;5NMG-01�9;7470+JK8Ai7a5N+PFSMGK8AQ7Z�6bR+^_�%h9;-0+2110MGAQ7a5N+21e9;F6F658KNcx9;74KNMGAE1�F6-:9;74KNOQ3E+21�MG{�MGA"3674K858KN1:+nc2+21�70+2c��6A6KNOQ3E+21xo�cx9;-�+J585N+21�1:MGAi7atT/JAE/J-:9;5N+JUP+JAQ7g74-0´21c2M�670+J3E10+21s+JA�70+JUgFE1|+J7)+JA¶+214FB9Gc2+]UP/JUPMGK8-0+^_

·h¸ � ��» ! É�Â�Æ ÀBÄ}É)Â��À�¿ � ¾;�Ai74-0+�5N+21Ht^-:9;UgUn9;K8-0+21 � XÏ9;7474-4K8\63E/2+21h+J7|5N+21Ht^-:9;UgUn9;K8-0+21Z9;7474-4K8\63E/2+21sMG{�5?>�MG-0<R-0+�<D>�/JLG9;583B9;74KNMGA!+2147OQ3E+J5Nc2MGAEOi3E+ô=MGA 74-0MG36LT+¶<D>@9;3674-0+21ncx9G1nMG{ 5?>�MG-0<R-0+�+2147P-0+J5d9;74K8LT+JUP+JAQ7nj?9GcJK85N+¶p�MG\670+JA6K8-�+J7np�UP+J7474-0++JA"+f36Lq-0+^_5;=A�FB9;-474KNcJ3658KN+J-xo6F6583E14KN+J36-01Ht^-:9;UgUn9;K8-0+21h9;7474-4K8\63E/2+21|92LT+2c]9;7474-4K8\636701 �E/J-4K870/21)F6-0/210+JAi70+JAQ7|5d9F6-0MGF6-4KN/J70/�Oi3E+n70MG3E1a5N+21e9;7474-4K8\636701 �E/J-4K870/21�AE+m<6/JF}+JAE<6+JAi7eOi3E+�<6+21e9;7474-4K8\636701�<6+21�14ÎqUa\}MG5N+21�p�5N+J36-ti9;3Ec��E+e<E9;AE1s5d9g-0´Jt^5N+�<6+aF6-0Mq<R3EcJ74KNMGA uwÎ�c2MGUgF6-4KN1s5N+�14ÎqUa\}MG5N+�+JA[FB9;-474KN+ati9;3Ec�E+�<6+�5d9g-0´Jt^5N+^_S�Z9;AE1c2+Zcx9G1xoR5?>�MG-0<R-0+]<D>�/JL^9;583B9;74KNMGA[<6+21s9;7474-4K8\636701)F}+J367)VJ74-0+f-0+JAE<R3¶c2MGUgFB9;74K8\65N+�9xLT+2cZ36A¶MG-0<R-0+]9G10c2+JAE<E9;AQ7<6+]cJ-0/x9;74KNMGA¶<6+21)A,+f3E<61x_�°±�E¥�¥~�E§w°;£��/:�R¦2¦x°G§w²I©�¤i£�ª 36AE+Zt^-:9;UgUn9;K8-0+�9;7474-4K8\63E/2+�+2147|<RK870+]*DXÏ9;7474-4K8\63E/2+�14KD70MG3679;7474-4K8\6367 �E/J-4K870/�<6+

Xj

o1 ≤ j ≤ n

o�<6+m5d9¶FB9;-474KN+�<R-0MGK870+�<D> 36AE+�-0´Jt^5N+m<6+mF6-0Mq<R3EcJ74KNMGAA→ X1, ..., Xn

AE+Z<6/JF}+JAE<�OQ3E+g��^_)<6+21s9;7474-4K8\636701s<6+21)10ÎQU�\SMG5N+21

X1, ...Xj−1

14K8743E/21|pgti9;3Ec��E+]<6+Xj

o6+J7�R_)<6+21s9;7474-4K8\636701 �E/J-4K870/21)<6+

A_

I9;-0c2+mOi3E+e5N+21Z-0´Jt^5N+21a10/JUn9;Ai74KNOQ3E+21a<6+21Zt^-:9;UgUn9;K8-0+21�*}XÏ9;7474-4K8\63E/2+21ajlMGAQ7�9;F6FB9;-:9��N74-0+P<6+21]<6/JF}+JARX<E9;AEc2+21�+JAi74-0+H9;7474-4K8\636701�<6+21IAEMGARX?70+J-4UgK8AB9;3Rb�<D> 36AE+.UPVJUP+`-0´Jt^5N+H9;K8AE14KqOi3,>�+JAQ74-0+C14ÎQU�\SMG5N+21�<D> 36AE+W-0´Jt^5N++J7Hc2+J3Rbm<R3�14ÎqUa\}MG5N+s+JA�FB9;-474KN+hti9;3Ec��E+Z<6+s5d9�UPVJUP+s-0´Jt^5N+ôqK85}+2147CK8UgFSMG-47:9;AQ7)<D>�/JLG9;583E+J-C5N+21.-0´Jt^5N+21)9;3jl36-s+J7ZpPUP+21436-0+�<6+]5d9n74-:92LT+J-01:/2+�<6+�5?>@9;-4\6-0+�<6+�<6/J-4K8L^9;74KNMGA,_A�sA[AE+aFS+J367f+JA!+>=D+J7h9;7470+JAE<R-0+e<D>@9xLTMGK8-FB9;-0c2MG36-43n70MG3670+)5d9fFB9;-474KN+|<R-0MGK870+)<6+)5d9f-0´Jt^5N+HF}MG36-`/JLG9;583E+J-`5N+21W9;7474-4K8\636701`cx9;-`5N+21W9;7474-4K8\636701<�E/J-4K870/21WAE+10+J-:9;KN+JAQ7�FB9G1I<RKN10FSMGA6K8\65N+21�F}MG36-��T+21�-0/2<R3EcJ74KNMGAE1�K8AQ70+J-4UP/2<RKd9;K8-0+21x_GIMG36-=+YbqF658KNcJK870+J-=c2+J7�MG-0<R-0+ô^MGA�3674K858KN10+36A�9;3674-0+PjlMG-4Un9;58KN14UP+n<6+P<6/Y�EA6K874KNMGA�<6+21]t^-:9;UgUn9;K8-0+21�*DXÏ9;7474-4K8\63E/2+21�OQ3E+g5?>�MGA�9;F6F}+J585N+P5N+21e��YÑR�Y�P�;�� l®4� � ��2�l� 3^� �

-��:��¤q¥~� �I£�¦x°±��©��^¦y§"!�� ª ¬|A&1:c��E/JUn9 <6+�74-:9G<R3EcJ74KNMGA�+2147�36AE+�t^-:9;UgUn9;K8-0+~AEMGARXc2MGAQ70+Ybq743E+J585N+|MG{P<6+21=9GcJ74KNMGAE1�10/JUn9;Ai74KNOQ3E+21xoT<6/J58K8UgK870/2+21�FB9;-�<6+21=9Gc2c2MG5d9G<6+21xoi10MGAi7�K8AE10/J-0/2+21<E9;AE1|5N+21HFB9;-474KN+21|<R-0MGK870+21|<6+21)-0´Jt^5N+21)<6+ZF6-0Mq<R3EcJ74KNMGA,_ �� £Q¥�� w£��$# ?.MGAE14KN<6/J-0MGAE1W5d9Zt^-:9;UgUn9;K8-0+h<6+21`+YbRF6-0+21014KNMGAE1C9;-4K87��6UP/J74KNOi3E+21.Oi3E+|AEMG3E1W9xLTMGAE1WK8AQ74-0M;X<R36K870+a9;3¶<6/J\6367s<6+Zc2+]c��B9;F6K874-0+m�

L → E �E → E � T | T

T → T � F | F

F → ( E - | n

¬sA[10c�E/JUn9n<6+a74-:9G<R3EcJ74KNMGA!OQ36K�-0/x9;58KN10+a5d9g-0+214ÎqAi7��E´21:+�<D> 36A!10MG36-0c2+�<6+aF6-0MGt^-:9;UgUP+�+2107s<6/Y�EA6K�<6+]5d9

�0� � AB9;58ÎR10+Z10/JUn9;AQ74KNOi3E+ôEt^-:9;UgUn9;K8-0+21h9;7474-4K8\63E/2+21s+J7)74-:9;AE1«j�MG-4Un9;74KNMGAE1Un9;A6KN´J-0+]1436K8L^9;Ai70+m�

L → E � { 19254 (�� - }E → E � { 19254 (�� - } T | T

T → T � { 13254 (�� - } F | F

F → ( { 192'4 (��(�� - } E - { 13254 (�� -�� - } | n { 13254 ( � & �'!(#$#(.:/ - }MG{ 13254 10K8tÂ6Kk�B+]K8UgF6-4K8UP+J-x_�?.MGAE10KN<6/J-0MGAE1|5d9�F"�6-:9G10+ D �(E"�0FG� <6MGAQ7|5?>@9;-4\6-0+a<6+Z<6/J-4K8L^9;74KNMGA[<6/2c2MG-0/�<6+219GcJ74KNMGAE1|1:/JUn9;Ai74KNOQ3E+21|+2147]�

�

��

��

��

��

��

NNNNNNNNNNNNNN

� ��

�

vvvv

vvvv

vvv

VVVVVVVVVVVVVVVVVVVVVVVVVVVVV

� � � ��

qqqqqqqqqqqqqq

VVVVVVVVVVVVVVVVVVVVVVVVVVVVV

� � � ��

qqqqqqqqqqqqq

� � �! �" " �� $#%�'&�(�)*),+.-��

�� / 0 �1�� $#%�'&�(�)*).+.-�� / �� $#%�'&�(�),),+.-��

*=>�MG-0<R-0+�<E9;AE1|5N+2OQ3E+J5�5N+21|-0´Jt^5N+21s1:/JUn9;Ai74KNOQ3E+21h1:MGAi7s/JL^9;583E/2+21h+2147s<6MGA6AE/aFB9;-|5N+]AQ36UP/J-0MmOQ36K�5N+J36-h+21479G1010MqcJKN/^_�?.+J5d9mc2MG-4-0+214F}MGAE<!pn36AE+�LQKN14K870+�<6+]ti9;3Ec�E+epm<R-0MGK870+�+JA[F6-0M;j�MGAE<6+J36-h<D>@9;\}MG-0<�<6+]5?>@9;-4\6-0+e<6+<6/J-4K8L^9;74KNMGA,_2

*,+�F6-4K8AEcJK8FB9;5`92L^9;Ai7:9;tT+g<6+21ht^-:9;UgUn9;K8-0+21]*}XÏ9;7474-4K8\63E/2+21Z74KN+JAQ7]pmc2+�OQ3E+�5?>�MG-0<R-0+e<D>�/JL^9;583B9;74KNMGA~<6+219;7474-4K8\636701�1436K87��«3E1470+JUP+JAi7�c2+�FB9;-0c2MG36-01¶<6+[ti9;3Ec�E+"p�<R-0MGK870+�+JA F6-0M;jlMGAE<6+J36-¶<D>@9;\}MG-0< <6+�5?>@9;-4\6-0+<6+�<6/J-4K8L^9;74KNMGA,_=Í³5)1y>@9;t^K87P<D> 36A MG-0<R-0+�14K8UgF65N+�p!F6-0MGt^-:9;UgUP+J-x_W�h+�F6583E1yo�AEMG3E1n92LTMGAE1nLQ3 c2MGUgUP+JAQ75?>�/JL^9;583B9;74KNMGA&<6+21�9;7474-4K8\636701�10ÎQAQ7��E/J74KN10/21�FS+J367�10+�j�9;K8-0+�+JA -0+JUPMGAi7:9;Ai7¶5?>@9;-4\6-0+!<6+JF636KN1�5N+21mj�+J36K8585N+21�«3E10Oi3,>@pP5d9g-:9GcJK8AE+�+J7sc2MGUgUP+JAQ7hc2+J7fMG-0<R-0+a10+aUn9;-4KN+aFB9;-«j?9;K870+JUP+JAi7]pP5?>�MG-0<R-0+�<6+�cJ-0/x9;74KNMGA!<6+aA,+f3E<61<E9;AE1�36AE+W9;AB9;58ÎR10+`9G10c2+JAE<E9;AQ70+.<6+=7³ÎqFS+W*A%a_xÍÏ5Q1:+�74-0MG36LT+ÒQ3,>�MGAaF}+J367,j?9;K8-0+=c2MG585N+J-I5?>�MG-0<R-0+`<D>�/JL^9;583B9;74KNMGA<D> 36AE+Zt^-:9;UgUn9;K8-0+�*}XÏ9;7474-4K8\63E/2+�pgc2+J7)MG-0<R-0+a<6+]cJ-0/x9;74KNMGA!9G10c2+JAE<E9;AQ70+a<6+21HA,+f3E<61y_�MG36-=9;-4-4K8LT+J-�p|c2+J5d9)K85q10+`FSM^1:+`<6+J3Rb]F6-0MG\65N´JUP+21H�y<6/2cJ5N+JAEc�E+J-�5?>�/JLG9;583B9;74KNMGAg<6+21�-0´Jt^5N+21I1:/JUn9;Ai74KNOQ3E+215NMG-01�<6+!5d9�-0/2<R3EcJ74KNMGA&<D> 36AE+�FB9;-474KN+�<R-0MGK870+[LT+J-01�36AE+�FB9;-474KN+!ti9;3Ec�E+~<6+!-0´Jt^5N+!<6+�F6-0Mq<R3EcJ74KNMGA&+J7-0/2cJ36F}/J-0+J-�5N+21�L^9;5N+J36-01�<6+21g9;7474-4K8\636701 �E/J-4K870/21ecx9;5NcJ365N/21eF}MG36-�5N+21e14ÎqUa\}MG5N+21aF6583E1gp¶ti9;3Ec��E+�<E9;AE1�5d9-0´Jt^5N+P<6+gF6-0Mq<R3EcJ74KNMGAµulMG3~LT+JAB9;AQ7�<6+e5d9�FB9;-474KN+Pti9;3Ec��E+n<6+e5d9�-0´Jt^5N+yzY_32=MxÎTMGAE1�c2+21]<6+J3Rb�F6-0MG\65N´JUP+2170MG36-sp�70MG36-x_

�q_�� c�E/JUn9P<6+f74-:9G<R3EcJ74KNMGA ��

�� ! � � ��&! �� ,�$�� ! �� "� � � � ��&!�� f9;AE1�36AE+W9;AB9;58ÎR10+`9G10c2+JAE<E9;AQ70+ôy70MG3670+21�5N+21,-0´Jt^5N+21�10/JUn9;Ai74KNOQ3E+21I10MGAi7I/JLG9;583E/2+21�5NMG-01�<6+�5d9H-0/2<R3EcJ74KNMGA<D> 36AE+[FB9;-474KN+[<R-0MGK870+!<6+¶-0´Jt^5N+!<6+�F6-0Mq<R3EcJ74KNMGA LT+J-01m1�9�FB9;-474KN+[ti9;3Ec��E+^_C�Z9;AE1m36AE+¶t^-:9;UgUn9;K8-0+�*}X9;7474-4K8\63E/2+ZulMG3a36Ae10c��E/JUn9s<6+W74-:9G<R3EcJ74KNMGA�zYo;<6+21�-0´Jt^5N+21I<6MGK8LT+JAi7�VJ74-0+W/JL^9;583E/2+21�+JAi74-0+W5d9H-0+2c2MGA6AB9;KN101�9;AEc2+<6+g<6+J3Rb�14ÎQU�\SMG5N+21Z103Ec2c2+21014Kkj�1Z<E9;AE1Z5d9mFB9;-474KN+P<R-0MGK870+g<6+21Z-0´Jt^5N+21]<6+eF6-0Mq<R3EcJ74KNMGA,_AIMG36-aMG\670+JA6K8-]c2+J7+>=D+J7f9;3!UPMGUP+JAi7]<D> 36AE+�-0/2<R3EcJ74KNMGA,o}K85�143*)P7h<D> K8AQ74-0MQ<R36K8-0+eF}MG36-fc��B9GOQ3E+�-0´Jt^5N+�K8AQ70/J-4KN+J36-0+Ppn/JL^9;583E+J-36A"AEMGARX?70+J-4UgK8AB9;5C\6KN<6MGA,oI<6/J-4K8LG9;AQ7�5d9�F"�6-:9G10+PLqKN<6+ôI<6MGAi7�5N+P-��G5N+n1:+J-:9�36A6KNOQ3E+JUP+JAi7g<6+n<6/2cJ5N+JAEc�E+J-5?>�/JL^9;583B9;74KNMGA[<6+f5d9e-0´Jt^5N+]1:/JUn9;Ai74KNOQ3E+]Oi36KD5836K�+2147|9G1010MqcJKN/2+^_

�� £Q¥�� w£�� %|+JF6-0+JAEMGAE1g5?>�+Yb6+JUgF65N+�F6-0/2c2/2<6+JAQ7m<6+�5d9�14ÎqAi7��E´210+�<R3 1:MG36-0c2+^_<�MG36-mc��B9GOQ3E+�-0´Jt^5N+10/JUn9;AQ74KNOi3E+HOQ36KQA,>@9;F6FB9;-:9��N7�FB9G1�ps5d9)�EAe<6+W5d9sFB9;-474KN+C<R-0MGK870+.<6+.5d9|-0´Jt^5N+H<6+`F6-0Mq<R3EcJ74KNMGA,o^MGA�K8Ai74-0Mq<R36K8736A�AEMGARX?70+J-4UgK8AB9;5�\6KN<6MGA,oE<6/J-4K8LG9;AQ7ε9;3EOQ3E+J5�+2147|9G1:10MQcJKN/f5d9�-0´Jt^5N+]K8Ai70/J-4KN+J36-0+n�

L → E � { 192'4 (�� - }E → E � X T | T

X → ε { 13254 (�� - }T → T � Y F | F

Y → ε { 13254 (�� - }F → ( Z E - { 192'4 (�� -3� - } | n { 192'4 ( � & �'!$#(#$.0/ - }Z → ε { 13254 (��(�� - }

MG3670+21C5N+21C9GcJ74KNMGAE1C10MGAi7H9;5NMG-01Hp]5d9Z�EA�<6+21.FB9;-474KN+21C<R-0MGK870+21C<6+|-0´Jt^5N+21C<6+sF6-0MQ<R3EcJ74KNMGA,_ �sAmFS+J367C<6MGAEc5N+21=/JL^9;583E+J-`ph5d9h-0/2<R3EcJ74KNMGA,oic2MGUgUP+HF}MG36-�5N+21=9;7474-4K8\636701`10ÎQAQ7��E/J74KN10/21x_$�sAP-0+JUn9;-0OQ3E+)9;3E1014KEOQ3E+C5?>�MG-0<R-0+<D>�/JL^9;583B9;74KNMGAm<6+21=-0´Jt^5N+21`FSMG36-`36AE+|9;AB9;58Îq1:+)<6+H5d9fF"�6-:9G10+ D �$E �0FG� +2147=/2OQ36K8L^9;5N+JAi70+sp]c2+J585N+|<R3n10c�E/JUn9<6+Z74-:9G<R3EcJ74KNMGA�F6-0/2c2/2<6+JAQ7x_2

�� ,�$��0�� ! �0�#�#� ��%&��!"��! �� $ �� ! *�9[74-:9;AE1«jlMG-4Un9;74KNMGA F6-0/2c2/2<6+JAQ70+�+2147e74-0´21e14K8UgF65N+�p�-0/x9;58KN10+J-x_@;=585N+nj�MGAEcJ74KNMGA6AE+�1:9;AE1e<RK )ncJ365870/�14K5N+21g-0´Jt^5N+21P1:/JUn9;Ai74KNOQ3E+21n10+�\}MG-4AE+JAi7mp[j?9;K8-0+�<6+21P+>=D+J701g<6+�\}MG-0<Do�c2MGUgUP+�<E9;AE1g5N+�cx9G1gF6-0/2c2/2<6+JAQ7x_

?.+JF}+JAE<E9;Ai7xo,1x> K85�1x>@9;t^K87Z+>=D+2cJ74K8LT+JUP+JAi7a<D>�/JL^9;583E+J-]<6+21]9;7474-4K8\636701 �E/J-4K870/21xoD+J585N+e+2147fK8AE143*)n1�9;Ai70+^_�IMG36-c2MGUgF6-0+JAE<R-0+P5N+eF6-0MG\65N´JUP+ô�c2MGAE14KN<6/J-0MGAE1a<6+J3Rb�-0´Jt^5N+21a<6+eF6-0Mq<R3EcJ74KNMGA�9xLT+2cP<6+21Z-0´Jt^5N+21a1:/JUn9;Ai74KNOQ3E+219G1010MqcJKN/2+21]�A→ X Y ��& ! ) ��&��Y → A B � & ! ) � � & !MG{�!g+2147W36A�9;7474-4K8\6367 �E/J-4K870/h<6+ � +J7 � 9;5NMG-01WOQ3E+ � +2147W36A�9;7474-4K8\6367H14ÎqAi7��E/J74KN10/s<6+ � _i*,+|F6-0MG\65N´JUP+OQ36K)10+�FSM^10+�+2107eOQ3E+�5?>@9;7474-4K8\6367 !�<6+ � <6MGK87PVJ74-0+¶/JLG9;583E/�9xLG9;AQ7n<6+�c2MGUgUP+JAEc2+J-P5?>@9;AB9;58ÎR10+�<6+�5d9F}MG-474KNMGA�<6+nF"�6-:9G10+mOQ36K`L^9�VJ74-0+n-0/2<R36K870+�p � cx9;-xo�FB9;-�<6/Y�EA6K874KNMGA <D> 36AE+mt^-:9;UgUn9;K8-0+�*DXÏ9;7474-4K8\63E/2+ôc2+J7Z9;7474-4K8\6367hF}+J367sVJ74-0+�3674K858KN10/�<E9;AE1h5N+21|-0´Jt^5N+21f10/JUn9;AQ74KNOi3E+21Z9G1010MqcJKN/2+21f9;3Rb¶F6-0MQ<R3EcJ74KNMGAE1f<6+ � _ ;�AFB9;-474KNcJ3658KN+J-xoBMGA¶FS+J367H5?> 3674K858KN10+J-s<E9;AE1)5N+21H-0´Jt^5N+21)/JL^9;583B9;Ai7s5N+21|9;7474-4K8\636701|<6+ � MG3¶<6+"!|_*=> KN<6/2+¶KNcJKh+2147m<D> 3674K858KN1:+J-m5N+�j�9;K87�Oi3E+¶5d9�L^9;5N+J36-�<D>@9;7474-4K8\6367 ��& ! +2147�MG\670+JAi3E+!<RK8-0+2cJ70+JUP+JAi7�<6+5?>@9;7474-4K8\6367 ��&�� FB9;-�14K8UgF65N+[-0+2c2MGF6KN+¶F}MG36-�-0/2cJ36FS/J-0+J-�<RK8-0+2cJ70+JUP+JAi7�c2+J7470+[LG9;5N+J36-�<E9;AE1�5d9~F6K85N+!<6+5?>@9;AB9;58ÎR10+J36-m9G10c2+JAE<E9;AQ7x_ ;�A +>=D+J7xo�+JA 9;AB9;58ÎR10+¶9G10c2+JAE<E9;AQ70+ô`MGA -0+2c2MGA6AB9��N7m<D>@9;\}MG-0< 5d9!F}MG-474KNMGA <6+F"�6-:9G10+fc2MG-4-0+214F}MGAE<E9;Ai7|9;3�14ÎqUa\}MG5N+ � F636KN1.c2+J585N+fc2MG-4-0+214F}MGAE<E9;Ai7hp]5d9�F}MG-474KNMGA�<6+hF"�6-:9G10+f<6/J-4K8L^9;\65N+pgFB9;-474K8-Z<R3!14ÎQU�\SMG5N+ � _ ?.MGUgUP+�K85,j?9;367s-0+2c2MGA6AB9��N74-0+ec2+�Oi36KIc2MG-4-0+214FSMGAE<E9;AQ7]9;3!14ÎqUa\}MG5N+ � 9xLG9;AQ7<6+Z-0/2<R36K8-0+ZLT+J-01 � oEMGA�F}+J367)10+f-0+J74-0MG36LT+J-s<E9;AE1|5d9ec2MGAR�Et^36-:9;74KNMGA!<6+fF6K85N+a<D>@9;AB9;58Îq10+a1436K8LG9;AQ70+P�

�� AB9;58ÎR10+Z10/JUn9;AQ74KNOi3E+^oEt^-:9;UgUn9;K8-0+21h9;7474-4K8\63E/2+21s+J7)74-:9;AE1«j�MG-4Un9;74KNMGAE1

�� _8_8__8_8_

� 36F6FSM^10MGAE1�OQ3,>@p~c2+J7nK8AE107:9;Ai7xo.K85)j?9;K8585N+¶/JL^9;583E+J-n36AE+[-0´Jt^5N+�AE/2c2+21010K87:9;Ai7�5d9�L^9;5N+J36-�<6+ � & !�_W*,+14ÎqUa\}MG5N+ � A,>�+2147fFB9G1Z<E9;AE1h5d9mF6K85N+�Un9;KN1 � 5836KIÎ[+2147Z<6/ �4pR_}ÍÏ5I143*)P7Z<6MGAEce<6+�-0+JUgF65d9Gc2+J-]5?>@9Gc2c2´21]p��& !�FB9;-`36A�9Gc2c2´21.p]5?>@9;7474-4K8\6367 � <R3m10ÎQU�\SMG5N+ � F6-0/210+JAQ7W5836KS<E9;AE1`5d9ZF6K85N+^_(IMG36-.c2+J5d9RoQMGAn-0+JUn9;-0OQ3E+OQ3E+�5d9�FSM^10K874KNMGA <R3 14ÎqUa\}MG5N+ � <E9;AE1n5d9!F6K85N+�FB9;-P-:9;F6F}MG-47m9;3 10MGUgUP+J7n1:+J-:9�70MG3G�«MG36-01P5d9�UPVJUP+5NMG-010OQ3E+P5d9�-0´Jt^5N+n10/JUn9;AQ74KNOi3E+�<6MGK87�VJ74-0+m/JLG9;583E/2+!��p�5d9�F}M^14K874KNMGA�10MGUgUP+J7�X �^_ �sA"-0+JUgF65d9Gc2+�<6MGAEc<E9;AE1�5d9h-0´Jt^5N+H10/JUn9;AQ74KNOi3E+H5?>@9Gc2c2´21 ��& !]FB9;- 487 #$.�� ( 2$2 . �� &�� oG+JAg1436F6F}M^1:9;Ai7=OQ3E+.5?>�MGAgFS+J367`9xLTMGK8-9;K8AE14K�9Gc2c2´21h9;3¶c2MGAi70+JAQ3[<6+Z5d9�F6K85N+]c2MGUgUP+a1x> K85,1x>@9;t^KN101:9;K87s<D> 36A�7:9;\65N+x9;3,_ �� £Q¥�� w£�� %|+JF6-0+JAEMGAE1`5d9ht^-:9;UgUn9;K8-0+|<6+21=<6/2cJ5d9;-:9;74KNMGAE1.+J7`1:9f<6/Y�EA6K874KNMGA�<RK8-4K8tT/2+HFB9;-=5d9Z14ÎqAi7:9±b6+F}MG36-H5d9eF6-0MGFB9;ti9;74KNMGA[<R3�7ÏÎQF}+Z<6+21HL^9;-4Kd9;\65N+21a�

�-0Mq<R3EcJ74KNMGA %|´Jt^5N+]10/JUn9;AQ74KNOi3E+D → T L L &"��(4 .#! ) � T &$��(4 .T →

. +��87 . 6 T &"��(4 .*) � . + �87 . 6T → 6%� .$# T &"��(4 .*) �,6�� .$#L→ L1 � 7&� L1 &$� �$4 .#! ) � L &"��$4 .#!+J7 ! ')(#* � . 6 +��$4 . ( 7�� & . + �$6 .(. � L &$� �$4 .#! -L→ 7&� !�' (�* � . 6�+ �$4 . ( 7&� & . +��(6 .$. � L &$� �$4 .�! -

� 36-)5?>�+Yb6+JUgF65N+P> 6�� .$# 4 �� 6 >8oRAEMG3E1s9xLQKNMGAE1)MG\670+JAQ3¶5?>@9;-4\6-0+�<6+Z<6/J-4K8LG9;74KNMGA¶1036K8LG9;AQ7a�

� &� &$��(4 .*) �,6%� .$# D

kkkkkkkkkkkkkkkkkkkkkkkkk

TTTTTTTTTTTTTTTTTTTTTTTTTTTTT

� & * &"��(4 .#! ) � 6%� .(#D & ! ' (�* � . 6�+ �$4 . ( D � 6�� .(# -

TE & * &$� �$4 .#! ) �,6�� .$#

F@& !�' (#* � . 6�+��(4 . ( � � 6%� .$# - L

ssssssssssssss

LLLLLLLLLLLLLL

6 .$.$# L

ssssssssssssss

KKKKKKKKKKKKK� 7&� 3

� & * &$� �$4 .#! ) �,6�� .$# & !�' (#* � . 6�+��(4 . ( � � 6�� .$# - L � 7&� 2

7�� 1

2=MxÎTMGAE1Wc2MGUgUP+JAi7`1:+CFB9G1010+.5?>@9;AB9;58Îq1:+)9G10c2+JAE<E9;Ai70+s+J7=c2MGUgUP+JAi7=5?>�/JL^9;583B9;74KNMGAn<6+21�-0´Jt^5N+21=1:/JUn9;Ai74KNOQ3E+21\63670+JAi7h1436-H5?>@9;\E10+JAEc2+]<6+]5?>@9;7474-4K8\6367 �E/J-4K870/a<E9;AE1H5d9gF6K85N+g�

�q_�� c�E/JUn9P<6+f74-:9G<R3EcJ74KNMGA � �

�K85N+ @�6-:9G10+ �-0Mq<R3EcJ74KNMGA %s´Jt^5N+Z10/JUn9;Ai74KNOQ3E+-0/2+J5DF,oBO�oR--0/2+J5 F,oBO�oR-

u ��$4 . � 6%� .(#iz F,oBO�oR-T → 6%� .(# T &$� �$4 . ) � 6%� .(#

u ��$4 . � 6%� .(#izWF oBO�oR- u ��$4 . � 6%� .(#iz.* oBO�oR-

L→ 7�� ! ')(#* � . 6 +��(4 . ( 7��-& . + �$6 .$. � L &"��$4 .#! -� c2+J7470+�/J7:9;F}+ôIMGA�AE+mFS+J367�+YbR/2cJ3670+J-e5d9¶-0´Jt^5N+m1:/JUn9;Ai74KNOQ3E+�cx9;-�5?>@9;7474-4K8\6367L &$� �$4 .#!�A,>�+2147�FB9G1<RKN14F}MGA6K8\65N+`1436-�5d9HF6K85N+^_��9;-�c2MGAQ74-0+`5d9HLG9;5N+J36-I<6+=5?>@9;7474-4K8\6367

T &"��(4 .6oy+J585N+ôy+2147�<RKN10FSMGA6K8\65N+.9;3�<6+J3RbRKN´JUP+14ÎqUa\}MG5N+�+JA FB9;-47:9;AQ7�<R3 1:MGUgUP+J7n<6+�5d9�F6K85N+^_ � 36F6FSM^10MGAE1mOi3E+�5?>�MGA F636KN1010+�3674K858KN1:+J-n36AE+�j�MGAEcJ74KNMGA!��:. � . 6 � 7 #$.�9xLT+2ce36A"9;-4t^36UP+JAi7a+JAQ74KN+J-a<6MGA6AB9;Ai7]5N+e14ÎqUa\}MG5N+Pp�9Gc2c2/2<6+J-�pmFB9;-474K8-]<R3~10MGUgUP+J7]<6+5d9�F6K85N+ôEMGA�F}+J367H-0/2/2cJ-4K8-0+]5d9�t^-:9;UgUn9;K8-0+�9;7474-4K8\63E/2+]F6-0/2c2/2<6+JAQ70+a<6+Z5d9�j?9Gr2MGA¶1436K8L^9;Ai70+P�

�-0MQ<R3EcJ74KNMGA %s´Jt^5N+Z10/JUn9;Ai74KNOQ3E+D → T LT →

. + �87 . 6 T &"��$4 . ) � . +�� 7 . 6T → 6�� .$# T &"��$4 . ) �,6�� .(#L→ L1 � 7�� !�' (�* � . 6�+ �$4 . ( 7&� & . +��(6 .$. � !��0. � . 6 � 7 #$. ( E - &$� �$4 . -L→ 7�� !�' (#* � . 6�+��(4 . ( 7��-& . +��$6 .$. � !��:. � . 6 � 7 #$. ( � - &$� �$4 . -

*,+21|-0´Jt^5N+21)<6+Z-0+2c2MGF6KN+]/J7:9;AQ7s<6+JLT+JAi3E+aK8Ai3674K85N+21xo�MGA�5N+21s9e14K8UgF65N+JUP+JAQ7s/J58K8UgK8AE/2+21x_ 2=MGKNcJK�c2MGUgUP+JAi7h10+FB9G1010+]9;5NMG-01|5?>@9;AB9;58Îq1:+]9G10c2+JAE<E9;Ai70+m��K85N+ @�6-:9G10+ �-0Mq<R3EcJ74KNMGA %s´Jt^5N+]10/JUn9;Ai74KNOQ3E+-0/2+J5�F,oEO�oq--0/2+J5 F,oEO�oq-Tu ��(4 . �,6�� .$#iz F,oBO�oq-

T → 6%� .$# T &$� �$4 . ) �,6�� .(#Tu ��(4 . �,6�� .$#izWF oBO�oq-

Tu ��(4 . �,6�� .$#iz.* oBO�oq-

L→ 7�� ! ')(#* � . 6 +��$4 . ( 7�� & . + �$6 .(. �!��0. � . 6 � 7 #(. ( � - &"��$4 . -Tu ��(4 . �,6�� .$#iz.*µo O�oq-

Tu ��(4 . �,6�� .$#iz.*µo6O oR-

Tu ��(4 . �,6�� .$#iz.* oR-

L→ L1 �>7�� !�' (#* � . 6�+��(4 . ( 7��-& . +��$6 .$. �!��0. � . 6 � 7 #(. ( E - &"��$4 . -Tu ��(4 . �,6�� .$#iz.*µo -

Tu ��(4 . �,6�� .$#iz.*µoR-

Tu ��(4 . �,6�� .$#iz.* L→ L1 �>7�� !�' (#* � . 6�+��(4 . ( 7��-& . +��$6 .$. �!��0. � . 6 � 7 #(. ( E - &"��$4 . -

�sAnAEMG70+hOQ3E+)5N+21W-0´Jt^5N+21W10/JUn9;AQ74KNOi3E+21C/J7:9;AQ7./JL^9;583E/2+21,�«3E1470+h9;3nUPMGUP+JAi7H<6+|5d9Z-0/2<R3EcJ74KNMGA,oq5N+)AEMGU�\6-0+FB9G1010/Z+JA�FB9;-:9;UP´J74-0+�p�5d9�jlMGAEcJ74KNMGA !��0. � . 6 � 7 #(.gc2MG-4-0+214F}MGAE<�\6KN+JA[pec��B9GOQ3E+fj�MGKN1|p�5d9�F}M^14K874KNMGA¶<R314ÎqUa\}MG5N+ � <E9;AE1|5d9�F6K85N+^_2

*�9�70+2c��6A6KNOQ3E+]<D>@9Gc2c2´21)<E9;AE1H5d9�F6K85N+Z+2147C\6KN+JA¶9G<E9;F670/2+ap�\}+x9;3Ec2MG36F¶<6+ht^-:9;UgUn9;K8-0+21|*}XÏ9;7474-4K8\63E/2+21MG{�5N+21)9;7474-4K8\636701 �E/J-4K870/21|10MGAi7)10MG36LT+JAQ7)MG\670+JAi3E1|FB9;-)<6+21C-0´Jt^5N+21)<6+f-0+2c2MGF6KN+]<D>@9;7474-4K8\636701)14ÎqAi7��E/J74KN1:/21x_�9;-�c2MGAQ74-0+ôCc2+J7470+[70+2c�6A6KNOi3E+!K8UgF}M^10+!Oi3E+¶5N+[14ÎqUa\}MG5N+!Oi3E+[5?>�MGA <6MGK87�9Gc2c2/2<6+J-�<E9;AE1�5d9~F6K85N+!10MGK8770MG3G�4MG36-01�p�<RKN107:9;AEc2+��6b6+�FB9;-n-:9;F6F}MG-47�9;3 10MGUgUP+J7m<6+�5d9�F6K85N+^_ ?.+¶A,>�+2147nUn9;5 �E+J36-0+J3E1:+JUP+JAi7�FB9G170MG3G�4MG36-01)5N+Zcx9G1x_8?.MGAE14KN<6/J-0MGAE1s5d9�t^-:9;UgUn9;K8-0+a*DXÏ9;7474-4K8\63E/2+a1436K8L^9;Ai70+P�

� � � AB9;58ÎR10+Z10/JUn9;AQ74KNOi3E+ôEt^-:9;UgUn9;K8-0+21h9;7474-4K8\63E/2+21s+J7)74-:9;AE1«j�MG-4Un9;74KNMGAE1�-0Mq<R3EcJ74KNMGA %s´Jt^5N+Z10/JUn9;Ai74KNOQ3E+S →

!A C C & ! ) � A &��

S → + A B C C & ! ) � A &��C → D D & ! ) �� ( C & ! -

*,+�F6-0MG\65N´JUP+�OQ36K)10+�F}M^10+�KNcJK)+2147POQ3E+�5NMG-01P<6+�5?>�/JLG9;583B9;74KNMGA <6+�5d9!-0´Jt^5N+�10/JUn9;AQ74KNOi3E+D & ! ) �

� ( C & ! - o2MGAac�E+J-0c��E+CpC-0+JUgF65d9Gc2+J- C & !sFB9;-,36A�9Gc2c2´21�9;3�14ÎQU�\SMG5N+ A <E9;AE1,5d9HF6K85N+^_��!9;5 �E+J36-0+J3E1:+JUP+JAi7xoMGA�F}+J367)10+f74-0MG36LT+J-|<E9;AE1s<6+J3Rb�cx9G1)<6+Z�Et^36-0+P�� 10MGK87C5?>@9;AB9;58Îq1:+s70+JAQ70+]<6+h-0+2c2MGA6AB9��N74-0+a92LT+2cf5d9�F6-0+JUgKN´J-0+f-0´Jt^5N+Z<6+hF6-0Mq<R3EcJ74KNMGA¶1436- S oR+J7)9;5NMG-01H5N+14ÎqUa\}MG5N+

A+2147H5N+Z<6+J3RbRKN´JUP+]14ÎqUa\}MG5N+]<E9;AE1H5d9gF6K85N+ô

� 10MGK87f5?>@9;AB9;58Îq1:+�70+JAQ70+g<6+�-0+2c2MGA6AB9��N74-0+n92LT+2ce5d9�<6+J3RbRKN´JUP+e-0´Jt^5N+g<6+�F6-0Mq<R3EcJ74KNMGA~1436- So}+J7]9;5NMG-015N+Z14ÎqUa\}MG5N+

A+2147H5N+]74-0MGKN14KN´JUP+]14ÎqUa\}MG5N+Z<E9;AE1)5d9�F6K85N+^_

?.MGUgUP+�MGA�<6MGK87P92LTMGK8-g36AE+�10+J365N+�-0´Jt^5N+�10/JUn9;AQ74KNOi3E+�9G101:MQcJKN/2+�p�36AE+�F6-0Mq<R3EcJ74KNMGA,o�MGA AE+mF}+J367FB9G1Z-0+JUgF65d9Gc2+J-C & ![p�5d9mj�MGKN1ZFB9;- !��:. � . 6 � 7 #$. (�� - &�� +J7ZFB9;- !��:. � . 6 � 7 #$. ( D - &�� _D�f9;AE1ac2+gcx9G1xo5?>@9±�4MG367s<D> 36A!AEMGARX?70+J-4UgK8AB9;5IUn9;-0OQ3E+J36-|F}+J367s1:MG583674KNMGA6AE+J-s5N+aF6-0MG\65N´JUP+^_�?.MGAE10KN<6/J-0MGAE1|5d9Pt^-:9;UgUn9;K8-0+*}XÏ9;7474-4K8\63E/2+aUPMQ<RKk�B/2+P�

=-0MQ<R3EcJ74KNMGA %|´Jt^5N+]10/JUn9;AQ74KNOi3E+S →

!A C C & ! ) � A &��

S → + A B M C M & ! ) � A &��C & ! ) � M &��

M → ε M &�� ) � M & !C → D D & ! ) �� ( C & ! -

ÍÏcJK?oRK85,<6+JLqKN+JAi7HF}M^1014K8\65N+Z<6+f-0+JUgF65d9Gc2+J-M & !mFB9;- A &�� o6c^>�+2147«XÏp±X³<RK8-0+ !��0. � . 6 � 7 #$. ( � - &�� cx9;-H5NMG-01<6+)5d9a-0/2<R3EcJ74KNMGA�<6+

εLT+J-01

MoT5N+h14ÎqUa\}MG5N+

A10+|74-0MG36LT+sK8UgUP/2<RKd9;70+JUP+JAQ7)10MG3E1W5N+|14ÎqUa\}MG5N+

BOQ36K�+2107+JAn10MGUgUP+J7W<6+CF6K85N+^_i�f+CUPVJUP+ôTMGAPF}+J367=-0+JUgF65d9Gc2+J-

C & !]FB9;- A &�� +J7 M &�� 1:+J5NMGAg5N+)cx9G1xoTc^>�+2147«XÏp±X³<RK8-0+pPc�B9GOi3E+]jlMGKN1|FB9;- !��:. � . 6 � 7 #$. ( � - &�� cx9;-s<E9;AE1|5N+21|<6+J3Rb¶cx9G1|<6+]�Et^36-0+ô M MG3 A10+]74-0MG36LT+JAi7Z+JA<6+J3RbRKN´JUP+ZFSM^10K874KNMGA[peFB9;-474K8-|<R3¶1:MGUgUP+J7|<6+ZF6K85N+Z5NMG-01)<6+]5?>�/JLG9;583B9;74KNMGA!<6+f5d9e-0´Jt^5N+^_ ;�A¶+JA65N+JL^9;Ai7s5N+21-0´Jt^5N+21|<6+f-0+2c2MGF6KN+�<6+JLT+JAi3E+21|K8Ai3674K85N+21xo�MGA�MG\674KN+JAi7h9;5NMG-01|5d9�t^-:9;UgUn9;K8-0+�9;7474-4K8\63E/2+�1436K8LG9;AQ70+P�

�-0Mq<R3EcJ74KNMGA %s´Jt^5N+Z10/JUn9;Ai74KNOQ3E+S →

!A C

S → + A B M CM → ε M &�� ) � !��:. � . 6 � 7 #$. (�� - &��C → D D & ! ) �� ( !��:. � . 6 � 7 #(. (�� - &�� -

� ��

� ��'|(�� ( �� (��&��

*�9�F}MGF6365d9;-4K870/¶<D> � �[*%74KN+JAi7�p�5?> K8AE<6/JF}+JAE<E9;AEc2+!<6+21m<6MQcJ36UP+JAQ701m<6+¶5d9!j?9Gr2MGAµ<6MGAi7mK85N1n10+J-0MGAQ7F6-0/210+JAQ70/21)MG3�+YbqF65NMGK870/21y_q*`> K8ARjlMG-4Un9;74KNMGA¶+2107H\B9;58KN10/2+f10/JUn9;Ai74KNOQ3E+JUP+JAi7xo�c2+ZOi36K}F}+J-4UP+J7C<6+f5d9�-0+JF}/J-0+J-j?9GcJK85N+JUP+JAi7Z<E9;AE1h36A[<6MqcJ36UP+JAi7PuwFB9G1h\S+210MGK8A!<D>@9;AB9;58Îq1:+a5N+YbRKNcx9;5N+�MG3�14ÎqAi7:9±bRKNOi3E+aFSMG36-fc2+Zj?9;K8-0+yzY_S*�9F636KN101:9;AEc2+.<6+ � �!*�74KN+JAi7�<6MGAEc.p|5d9Cj?9GcJK858K870/H92LT+2c.5d9GOQ3E+J585N+WMGA�LG9)FSMG36LTMGK8-�-0/2cJ36F}/J-0+J-I<6+W5?> K8ARj�MG-4Un9;74KNMGA<E9;AE1s36A!<6MqcJ36UP+JAi7Z<6+]Un9;A6KN´J-0+gpP5?>�+YbqF65NMGK870+J-xoSF}MG36-|5d9nF6-0/210+JAi70+J-fMG3[F}MG36-|F6-0Mq<R36K8-0+�<6+aAEMG36LT+x9;3Rb<6MqcJ36UP+JAi701 � �!*=_iÍÏ5E+YbRKN1470+)<6+J3RbPt^-:9;AE<6+21C9;F6F6-0MQc�E+21`F}MG36-=74-:9;K870+J-`5N+21W<6MQcJ36UP+JAQ701 � �!*"�^5d9Z74-:9;AE1«Xj�MG-4Un9;74KNMGA¶<6+Z<6MQcJ36UP+JAQ7hp�FB9;-474K8-|<D> 36A�5d9;A6ti9;tT+a<6+ �B9;367)A6K8LT+x9;3¶c2MGUgUP+ � � *~+J7H5N+f74-:9;K870+JUP+JAi7f<6+<6MqcJ36UP+JAi7|c2MGUgUP+Z36A¶9;-4\6-0+Z<6+fUn9;A6KN´J-0+]F6-0MGt^-:9;UgUn9;74KNOi3E+aLQKd9�5?> � =Í`�� _�(sMG3E1s9;585NMGAE1HLTMGK8-)c2+21<6+J3Rb¶9;F6F6-0MQc�E+21s<E9;AE1hc2+]c�B9;F6K874-0+ô�+JA�UP+J747:9;AQ7s5?>�+JUgF"�B9G1:+a1436-)5d9PF6-0M2bRK8UgK870/�9xLT+2ca5N+21|t^-:9;UgUn9;K8-0+219;7474-4K8\63E/2+21=MG3g+JAe3674K858KN1:9;Ai7=c2+21�<6+J-4A6KN´J-0+21=FSMG36-�<6/Y�EA6K8-=<6+21�74-:9;K870+JUP+JAi701W+2)ncx9Gc2+21�1436-�5N+21�<6MQcJ36UP+JAQ701x_

� ¸�¹ ��Æ Ê:É)¾�Å|É)Å)Æ Â�Æ ÀBÄ}É)¾�Á��HÄ�� ÉCÀ�¿��|¾��

*�9)5d9;A6ti9;tT+.<6+=74-:9;AE14jlMG-4Un9;74KNMGA � � *�u � �[*�147ÏÎQ5N+21��E+2+J7�5d9;A6t^3B9;tT+yz�+2147,36A�5d9;A6ti9;tT+`F}+J-4UP+J747:9;Ai7�<6+F6-0MGt^-:9;UgUP+J-`<6+21�74-:9;AE14jlMG-4Un9;74KNMGAE1=<6+H<6MqcJ36UP+JAi701hulc��B9;A6tT+JUP+JAQ701W<6+H1474-43EcJ7436-0+yzIMG3P<6+21=74-:9G<R3EcJ74KNMGAE1<6+f<6MQcJ36UP+JAQ701HLT+J-01H<D>@9;3674-0+21.j�MG-4Un9;701]uw70+Ybq70+ô"! �[*òq+J70c^_ zY_ � � *"9�/J70/Z<D>@9;\SMG-0<�<6/Y�EA6K,c2MGUgUP+f36A5d9;A6ti9;tT+sFS+J-4UP+J747:9;AQ7C<6+|74-:9G<R36K8-0+|36A�<6MqcJ36UP+JAi7 � �!*[+JAm36AE+)j�MG-4UP+)K8UgF6-4K8Un9;\65N+fMG3mF6-0/210+JAi7:9;\65N+Zp36An3674K858KN1�9;70+J36-xoi<D>�MG{m1:MGAPAEMGU <6+|5d9;A6ti9;tT+|<6+Hj�+J36K8585N+21`<6+s147³Îq5N+21x_GIMG36-47:9;Ai7xoq5N+21.cJ-0/x9;70+J36-01W<6+ � � *[10+10MGAQ7|LqK870+Z-0+JAE<R3E1sc2MGUgF670+�<6+]5d9eF636KN1:1:9;AEc2+a+J7h<6+Z5d9gF}MG-470/2+Z\}+x9;3Ec2MG36F[F6583E1|5d9;-4tT+a<D> 36A¶70+J5�5d9;A6ti9;tT+<6+Z74-:9;AE1«j�MG-4Un9;74KNMGA,_� 3G�4MG36-0<D> �i36K?oH5d9�74-:9G<R3EcJ74KNMGA%<D> 36A&<6MQcJ36UP+JAQ7 � �!* LT+J-01�36AE+!j�MG-4UP+�K8UgF6-4K8Un9;\65N+~+2147�F658367��G7-0/x9;58KN10/2+hpZ5?>@9;KN<6+h<6+21�? �"� u 7$#��;� �0� � �v�q %��l�G�8�&%EÑR�0�J� 96zYoQ36AE+)AEMG-4UP+hc2MGAEcJ36-4-0+JAi70+f<6/JLT+J5NMGF6F}/2+s14F}/2cJKk�6XOQ3E+JUP+JAi7.FSMG36-.c2+J5d9R_ � � *[+2147`F658367��G7W3674K858KN10/|FSMG36-`5N+21`74-:9;AE1«j�MG-4Un9;74KNMGAE1.<6+|<6MqcJ36UP+JAi701xoQ\6KN+JAmOQ3,> 36AE+AEMG-4UP+¶u � � *}X � ��oDF}MG36-(' 3G®��P�^��l�w�Q"3Q¯*)2� �2�w�±zfF}+J-4UP+J7474-:9�\6KN+JAi7��G7a<6+e-0/x9;58KN1:+J-]<6+21Z74-:9;AE1«j�MG-4Un9;74KNMGAE1LT+J-01|<6+21s<6MQcJ36UP+JAQ701)j�MG-4Un9;7470/21s9xLT+2c]36AE+Zt^-:9;AE<6+]�EAE+21010+Z70MG367s+JA�F6-0M;�E7:9;Ai7f<6+Z70MG3670+Z5d9eF636KN1:1:9;AEc2+<6+ � � *=_¬|A[F6-0MGt^-:9;UgUP+ � � *�10+ZF6-0/210+JAQ70+�1:MG3E1)5d9ej�MG-4UP+�<D> 36A[+JAE10+JU�\65N+�<6+a-0´Jt^5N+21s<6+a74-:9;AE1«j�MG-4Un9;74KNMGA,_¬sAE+Z-0´Jt^5N+a<6+Z74-:9;AE14jlMG-4Un9;74KNMGA�14F}/2cJKk�B+ZFB9;-|36A��E5874-0+a5N+21)A,+f3E<61h<D> 36AE+�9;-4\}MG-0+210c2+JAEc2+a<6+a<6MQcJ36UP+JAQ79;3Rb6Oi3E+J5N1W+J585N+)1x>@9;F6F658KNOQ3E+|<E9;AE1=5N+|<6MQcJ36UP+JAQ7W10MG36-0c2+^_(;�585N+|<6MGA6AE+)+JAE1036K870+)36AE+Cj�MG-4UP+spftT/JAE/J-0+J-.<E9;AE15N+g<6MqcJ36UP+JAi7acJK8\65N+^_ �sA"9;36-:9;K87aF63~<6/Y�EA6K8-]A,> K8UgFSMG-470+nOi3E+J585N+g14ÎqAi7:9±b6+g14F}/2cJKk�BOi3E+eF}MG36- � � *òDUn9;KN1<E9;AE1I5?>�+214F6-4K87�<6+�� !*=oyK856/J7:9;K87IK8Ai70/J-0+2101�9;Ai7=<6+C<6/Y�EA6K8-�5N+21�F6-0MGt^-:9;UgUP+21 � � *�c2MGUgUP+C<6+21�<6MQcJ36UP+JAQ701

� �[*=_ � � *�+2147h<6MGAEca36A[5d9;A6ti9;tT+�pP\B9;58KN10+21sOQ3E+]5?>�MGA!F}+J367s<6/Y�EA6K8-hFB9;-|36AE+�� e_�¬|AE+a-0´Jt^5N+ � � *10+fF6-0/210+JAQ70+a<6MGAEc]1:+J5NMGA�5d9�jlMG-4UP+]1036K8LG9;AQ70+P�

�� -:9;AE1«jlMG-4Un9;74KNMGAE1h<6+Z<6MqcJ36UP+JAi701 � �!*� / � #<) � . 254 #$! � . 2 ! � � ! �� `� �l®0� ��' 3G®Y�n�� / � #@) � . 2'4 #$! � . �*,MG-01�<R3eFB9;-0c2MG36-01�<D> 36AP<6MQcJ36UP+JAQ7�FB9;-I5N+WUPMG70+J36-=<6+.74-:9;AE1«j�MG-4Un9;74KNMGA,oG5N+`�E5874-0+C<6/2cJ5N+JAEc�E+H5?>@9;F6F658KkXcx9;74KNMGA[<D> 36AE+a-0´Jt^5N+]5NMG-010OQ3,> 36A�A,+f3E<¶-0+JAEc2MGAi74-0/�c2MG-4-0+214FSMGAE<!9;3��E5874-0+^_B*�+Z�E5874-0+]+2147|36AE+a+YbRF6-0+21014KNMGA10+J5NMGA�5d9�AEMG-4UP+ � � !�_<?.+J7470+nAEMG-4UP+�F}+J-4UP+J7�<6+�<6/214K8tÂE+J-e36A"A,+f3E< <E9;AE1�36A 9;-4\6-0+ � �[* +JAj�MGAEcJ74KNMGAm<6+)10MGAn7³ÎqFS+)<D>�/J5N/JUP+JAQ7xoq5d9fF6-0/210+JAEc2+|<D> 36A�c2+J-47:9;K8A�9;7474-4K8\6367.MG3m<6+H5d9fL^9;5N+J36-W<D> 36A�9;7474-4K8\6367xo<6+21HA,+f3E<61)jw-0´J-0+21xoE9G1:c2+JAE<E9;Ai701hMG3�<6+210c2+JAE<E9;Ai701euw7³ÎqFS+Z<D>�/J5N/JUP+JAQ7xoS9;7474-4K8\636701sMG3�L^9;5N+J36-01xo6+J70c^_ zY_�,� 4R�G®J�l�?� �`� �l®0� � �a�k�m®��G�N�

� � !µ+2107I36Ae5d9;A6ti9;tT+C74-0´21�F636KN101�9;Ai7=OQ3E+WAEMG3E1�A,>@9;585NMGAE1=FB9G1�/J743E<RKN+J-=+JAP<6/J7:9;K85?_^¬|AE+C+YbRF6-0+21014KNMGA� � !�+2147)c2MGUgF}M^10/2+P�� <6+ �³�Y®��n�� 4*3;��l�l� 3G�E�S�Y�n�Y��oWOQ36K]<6/Y�EA6KN1010+JAQ7�36AE+�FSM^14K874KNMGA -0+J5d9;74K8LT+"9;3 A,+f3E<Èc2MG36-:9;AQ7xoc2MGUgUP+ZFB9;-|+Yb6+JUgF65N+Z5N+21C�E5N1)<D> 36A¶A,+f3E<�FB9;- � ! 7 # � �� <6+ �=�k�l®0��mK8AQ74-0MQ<R36K8701�FB9;-a5?>�MGF}/J-:9;70+J36-�>�)$):>8o�Oi36KWF6-0/2cJKN10+JAi7g<6+21�cx9;-:9GcJ70/J-4KN1474KNOi3E+21e<D> 36A�A,+f3E<Doc2MGUgUP+ZFB9;-|+Yb6+JUgF65N+Z5N+fAEMGU <6+Z5?>�/J5N/JUP+JAQ7�EF636KN1� <6+|F6-0/2<RKNcx9;701HMGF674KNMGA6AE+J5N1.F6-0/210+JAQ70/Z+JAi74-0+fcJ-0Mqc��E+J701COi36K}10MGAQ7.<6+21C+YbRF6-0+21014KNMGAE1.5NMGt^KNOi3E+21Wj�MG-4UP/2+211436-�36A 5d9;A6ti9;tT+�<6+[F6-0/2<RKNcx9;701¶14FS/2cJKk�BOQ3E+JUP+JAi7�<6/Y�EA6KZF}MG36- � � *òHc2MGUgUP+�FB9;-�+Yb6+JUgF65N+�5d9FSM^10K874KNMGA�<D> 36A¶/J5N/JUP+JAi7|�E5N1HFB9;-)-:9;F6F}MG-47sp�5?>�+JAE10+JUa\65N+�<6+21C�E5N1|<D> 36A¶A,+f3E<D_

�� £Q¥�� w£A�� *=>�+YbRF6-0+21014KNMGA � � ! � ! 7 # � )$) � !'! 487��$6 .�� 4 ( �(7��87 ( + ( - � D � 10/J5N+2cJ74KNMGA6AE+a36A[A,+f3E<92Îi9;AQ7|36A�/J5N/JUP+JAQ7H�E5N1au � ! 7 # � z.<6+fAEMGU � !"! 4 7 �$6 .g<6MGAQ7)5d9�FSM^10K874KNMGA�FB9;-4UgK,5N+21)9;3674-0+21H�E5N1H+2147��R_ 2*,+21CF6-4K8AEcJK8FB9;3RbmK8AE<RKNcx9;70+J36-01)<6+hF}M^14K874KNMGA�-0+J5d9;74K8LT+ � � !Ã10MGAQ7Z� ��! 7 # � o � . � �0. + � ! + � o 4 ! 6 . + � o! + �:. �� ( 6 o 4(6 .��:. �87�+ � o� �($#$# (�� 7�+ � +J7 ! ��$6 7 + * � .E_T�e>@9;3674-0+21W+YbRKN1470+JAQ7x_i*,+C�E5874-0+ � � ! F}+J367`VJ74-0+36A�AEMGU <D>�/J5N+JUP+JAi7xoR36A�AEMGU <D>@9;7474-4K8\6367xoR5N+|FB9G101:+YX?FB9;-470MG367]> � >}uwFSMG36-C70MG367HMG\R�«+J7H<6+sUPVJUP+fAB9;7436-0+yzYo36A�AEMGU <D>�/J5N/JUP+JAi7�MG3~<D>@9;7474-4K8\6367�9G1010MqcJKN/gp�36A�F6-0/2<RKNcx9;7a+JAi74-0+gcJ-0Mqc��E+J701x_�*,+21fF6-0/2<RKNcx9;701a10MGAQ7]<6+21+YbRF6-0+21014KNMGAE1]<E9;AE1a5N+210Oi3E+J585N+21�MGA~F}+J367Z3674K858KN10+J-a5N+21]MGF}/J-:9;70+J36-01]5NMGt^KNOQ3E+21��!+J7��SoD5N+21]MGF}/J-:9;70+J36-01<6+ec2MGUgFB9;-:9;KN10MGA � o � o � � o �0� o � +J7�� _A�sA!F}+J367a9;3E1014KI3674K858KN10+J-]<6+21Z+YbRF6-0+21014KNMGAE1Z9;-4K87��6UP/J74KNOQ3E+21a+J7<6+21Cj�MGAEcJ74KNMGAE1)F6-0/2<6/Y�EA6KN+21�ulc2MGUgUP+ 4 ( �(7��87 ( + ( - zY_(sMG70MGAE1)/Jti9;5N+JUP+JAQ7sOQ3E+f5d9�FB9;-474KN+f�E5874-0+Z<D> 36AE+Z-0´Jt^5N+Z<6+Z74-:9;AE14jlMG-4Un9;74KNMGA�F}+J367)VJ74-0+Zc2MGUgF}M^10/2+]<6+F6583E14KN+J36-01.+YbqF6-0+21:14KNMGAE1�� !&10/JFB9;-0/2+21WFB9;-W<6+21W\B9;-4-0+21WLT+J-474KNcx9;5N+21h> * >QOi36K�K8AE<RKNOi3E+JAQ7C5?>@9;5870+J-4AB9;74K8LT+^_*�9e-0´Jt^5N+a1x>@9;F6F658KNOi3E+�9;5NMG-01|pe70MG3670+21H5N+21|9;5870+J-4AB9;74K8LT+21|�E5874-0/2+21x_

�,� 4R�G®J�l�?� ' 3G®Y�n� � �]�8�n®��^�8�*�9�FB9;-474KN+ ' 3G®��n�n<6+e5d9�-0´Jt^5N+g+2147]c2MGAE1474K8743E/2+P<D> K8AE1074-43EcJ74KNMGAE1a<R3�5d9;A6ti9;tT+ � � * F}MG36-]c2MGAE1474-436K8-0+5d9�-0/21436587:9;7�<6+g5d9�74-:9;AE1«j�MG-4Un9;74KNMGA c2MG-4-0+214FSMGAE<E9;AQ7�9;3�A,+f3E<~10/J5N+2cJ74KNMGA6AE/mFB9;-]5N+e�E5874-0+n<6+P5d9�-0´Jt^5N+^_

?.+21hK8AE1474-43EcJ74KNMGAE1fc2MGUgFSMG-470+JAQ7Z<6+21sK8AE1074-43EcJ74KNMGAE1sF}+J-4UP+J747:9;Ai7Z5d9ncJ-0/x9;74KNMGA�<6+aA,+f3E<61f+J7f<D>@9;7474-4K8\636701ulc2MGUgUP+�/ � #@) .$#$. 2 . +�� +J7 / � #@) ! ��(687 + * � .izYoG<6+21�K8AE1474-43EcJ74KNMGAE1�F}+J-4UP+J747:9;Ai7=<6+C-0/2cJ36F}/J-0+J-�5N+Cc2MGAi70+JAQ3<6+W5?>�/J5N/JUP+JAi7`10MG36-0c2+fulc2MGUgUP+�/ � #@) �'!$#�*'. � (� Rz,+J7�<6+21IK8AE1474-43EcJ74KNMGAE1�F}+J-4UP+J747:9;Ai7=<D>@9;F6F658KNOQ3E+J-�-0/2cJ36-014KkXLT+JUP+JAi7�5N+21�-0´Jt^5N+21�<6+C74-:9;AE14jlMG-4Un9;74KNMGAP<R3eF6-0MGt^-:9;UgUP+ � � *�1436-�5N+21�A,+f3E<61I�E5N1�<R3eA,+f3E<g10+J5N+2cJ74KNMGA6AE/ulc2MGUgUP+ / � #@) ! 4$4 # � � � . 254 #$! � . � zY_ � � * <6/Y�EA6K87Z/Jti9;5N+JUP+JAi7a<6+21Z1074-43EcJ7436-0+21Z<6+�c2MGAQ74-��G5N+��D9;5870+J-4AB9±X74K8LT+21au�/ � #@) 7 �+J7 / � #@) ��!�( ( � .Qz.+J7)-0/JF}/J74K874KNMGA�u�/ � #@)� �( 6 � .$!�� !6zY_� ¯��x�Y� �:� � �a®��G�N� � ��l®«�^�6� ' 3G®Y�g�T�l� 3G�*,MG-010OQ3,> K85sA,> Î 9~FB9G1m<6+[-0´Jt^5N+¶<6+[74-:9;AE1«j�MG-4Un9;74KNMGA OQ36Kh1y>@9;F6F658KNOi3E+!p~36AµA,+f3E<µ<R3 <6MQcJ36UP+JAQ710MG36-0c2+ô � � *"9;F6F658KNOQ3E+]5?> 36AE+]<6+21|<6+J3Rb�-0´Jt^5N+21|FB9;-|<6/Yj�9;367)1036K8LG9;AQ70+21a�� ~ª *,+21�-0´Jt^5N+21�<6+n74-:9;AE1«jlMG-4Un9;74KNMGA 10MGAQ7e9;F6F658KNOQ3E/2+21a-0/2cJ36-010K8LT+JUP+JAi7np�70MG3E1�5N+21a<6+21:c2+JAE<E9;Ai701g<R3A,+f3E<D_

� _��]*,+f5d9;A6ti9;tT+�<6+f74-:9;AE1«j�MG-4Un9;74KNMGA � � * ��

� B�ª � KB5N+)A,+f3E<�c2MG36-:9;Ai7Hc2MGAQ74KN+JAi7H<R3n70+YbR70+|<6+|7³ÎqFS+�� + ��oq9;5NMG-01Wc2+|70+Ybq70+s+2147`-0+2c2MGF6KN/s70+J5�OQ3E+J5<E9;AE1|5N+Z<6MQcJ36UP+JAQ7scJK8\65N+^_%��l®Y� �x�l�Q®0� �� Q�S� 'x�Y�q�v�w�8� � %��?.MGUgUP+�70MG367¶<6MqcJ36UP+JAi7 � �!*=oC36AE+�j�+J36K8585N+ � � * c2MGUgFSMG-470+�36AE+"+JAi70VJ70+�j�MG-4UP/2+~<D>�/J5N/JUP+JAi701<6MGA6AB9;Ai7[<6+21�K8ARjlMG-4Un9;74KNMGAE1¶1436-�5?>�+JAE10+JUa\65N+�<R3 <6MqcJ36UP+JAi7x_ ?.+J7470+~+JAi70VJ70+~c2MGAQ74KN+JAi7�5?> K8AE1074-43EcJ74KNMGA

� � *[OQ36KEK8AE<RKNOQ3E+sOQ3,> K85B1x>@9;t^K87.<D> 36Am<6MqcJ36UP+JAi7H10+)c2MGARj�MG-4Un9;Ai7HpZ5d9]AEMG-4UP+ � � *=oi<6MGAQ7W5d9ZjlMG-4UP+)+2107s�� / � #@) �� #$. � !".$. � / 2 # + � ) / � # �� ! ��(4 ) �� & � D & ( 6 � � �� +(6 ! + � �( 6G2 ��". 6 �57 ( +(�� & � � �

;�585N+sFS+J367H9;3E1014KSc2MGUgFSMG-470+J-C36A�/J5N/JUP+JAi7�/ � #@) (#* �(4 * � <6MGAQ7C5N+|-��G5N+hc2MGAE14KN1470+fpZF6-0/2cJKN10+J-C5N+|jlMG-4Un9;7C<6+10MG-474KN+�<6+]5d9n74-:9;AE1«j�MG-4Un9;74KNMGA uw7ÏÎQF}+a<6+�<6MqcJ36UP+JAi7xo � �!*=o ! �!*=o�MG3[70+YbR70+ô�� ¼1y> K85I1x>@9;t^K87h<D> 36A<6MqcJ36UP+JAi7 � �!*=o6+J70c^_ zY_� F6-0´21,c2+J7470+`+JAi70VJ70+ôyMGAa74-0MG36LT+�36Aa+JAE10+JU�\65N+`<6+�-0´Jt^5N+21�<6MGA6AE/2+21�FB9;-�<6+21,/J5N/JUP+JAQ701 / � #@) � . 254 #(! � .6oF636KN1H5d9e\B9;58KN1:+hjl+J-4Un9;AQ70+a<6+Z5?>�/J5N/JUP+JAQ7 / � #@) �� #$. � !'.(. � o6c^>�+2147«XÏp±X³<RK8-0+ �� / � #@) �&�� #$. � !'.(. � � _

�.®Y�v� �J� 46�G�8�Y�]�v�6�J�l®��2�l� 3G�6� � %%�*,+21fF6-4K8AEcJK8FB9;5N+21ZK8AE1474-43EcJ74KNMGAE1 � � * 10MGAQ7h5N+21Z1036K8LG9;AQ70+21xoD92LT+2ce5N+21]9;7474-4K8\636701ZOQ36KI5N+J36-01Z1:MGAi7]9;747:9±Xc��E/21�� / � #@) ! 4(4 # � � � . 254 #$! � . �� 9;F6F658KNOQ3E+P-0/2cJ36-010K8LT+JUP+JAi7�5N+21]-0´Jt^5N+21a<6+n74-:9;AE1«j�MG-4Un9;74KNMGA�9;3Rb��E5N1<R3 A,+f3E< c2MG36-:9;Ai7x_<;�585N+�F}+J367P92LTMGK8-g36A 9;7474-4K8\6367 � .$#$.�� F}MG36-e-0+21474-0+JK8AE<R-0+�5?>�+JAE10+JU�\65N+�<6+21A,+f3E<61|9;3Rb6Oi3E+J5N1s+J585N+Z1x>@9;F6F658KNOi3E+^_� � / � #@) �'!(##*'. � (� � �}F6-0Mq<R36K87a5d9�LG9;5N+J36-a<6+e5?>�/J5N/JUP+JAQ7�MG3�<6+g5?>@9;7474-4K8\6367�9;3EOQ3E+J5`MGA~5?>@9;F6F658KNOQ3E+^_� MGAmc2MGUgF}MG-470+JUP+JAi7HL^9;-4KN+|+JAnjlMGAEcJ74KNMGA�<6+)5?>�MG\R�4+J7C9;3EOQ3E+J5}MGAn5?>@9;F6F658KNOQ3E+ �iF}MG36-`36A�/J5N+JUP+JAi7HMG336A¶9;7474-4K8\6367xoB+J585N+Z-0+J70MG36-4AE+]36AE+]c��B9��NAE+�<6+Zcx9;-:9GcJ70´J-0+]-0+JF6-0/210+JAQ7:9;Ai7h5N+Zc2MGAi70+JAi3�MG3�5d9eL^9;5N+J36-x_� � / � #@) � .0/ � � �R-0+JF6-0MQ<R36K87s10MGA�c2MGAi70+JAQ3!<E9;AE1H5N+a<6MQcJ36UP+JAQ7scJK8\65N+^_� � / � #@) �#( 4�� 6c2MGF6KN+Z5?>�/J5N/JUP+JAi7fc2MG36-:9;Ai7h<R3¶<6MqcJ36UP+JAi7s1:MG36-0c2+Z<E9;AE1)5?>@9;-4\}MG-0+210c2+JAEc2+a<R3¶<6MqcJ3RXUP+JAi7|cJK8\65N+muwUn9;KN1)FB9G1H5N+21C�E5N1yoRK85�1x>@9;t^K87)<6+]c2MGF6KN+]1036FS+J-«�BcJKN+J585N+yzY_� � / � #@) .$#(. 2 . +��,+ ! 2 . � � � � � �icJ-0/2+s36A�/J5N/JUP+JAi7H<6+|AEMGU��<E9;AE1.5?>@9;-4\SMG-0+210c2+JAEc2+f<R3�<6MQcJ36UP+JAQ7cJK8\65N+^_� � / � #@) ! � �$687 + * � . + ! 2 . � � � � � �Bpe5?> K8Ai70/J-4KN+J36-f<D> 36AE+]K8AE1074-43EcJ74KNMGA / � #@) .$#(. 2 . +�� oB9±�«MG3670+�pgc2+J7/J5N/JUP+JAi7]36A"9;7474-4K8\6367]<6+eAEMGU ��<6MGAi7]5d9�L^9;5N+J36-]+2147Z<6MGA6AE/eFB9;-Z5?>�/JL^9;583B9;74KNMGA"<R3~c2MGAi70+JAQ3�<6+5?> K8AE1474-43EcJ74KNMGA,_� � / � #@) 7 � . ��5�� 54 � � �Q10KS5?>�+YbRF6-0+21014KNMGA�\}MQMG5N/2+JA6AE+P� �24!+2147CLQ-:9;KN+ô69;5NMG-01C5N+fc2MGAi70+JAQ3¶<6+h5?> K8AE1«X74-43EcJ74KNMGA¶+2147)+Yb6/2cJ3670/ôB14K8AEMGA�-4KN+JA¶A,>�+2147Cj�9;K87x_� � / � #@) � !%(�( � . � �R+Yb6/2cJ3670+s5?> 36AE+ZMG3�5?>@9;3674-0+f<6+21CK8AE1474-43EcJ74KNMGA�<D>@9;5870+J-4AB9;74K8LT+21)OQ3,>�+J585N+Zc2MGAi74KN+JAQ7xoBp5d9gUn9;A6KN´J-0+�<D> 36AE+]K8AE1474-43EcJ74KNMGA �:! � .PtT/JAE/J-:9;58KN10/2+^_S*,+21|K8AE1074-43EcJ74KNMGAE1h<6+21f9;5870+J-4AB9;74K8LT+21hFS+J36LT+JAQ7VJ74-0+]<6+21Cj�MG-4UP+21)1436K8L^9;Ai70+21�� / � #@) � !". + � . ��(� � � �24 � � �R5N+]c2MGAi70+JAQ3[<6+Z5?>�/J5N/JUP+JAQ7s+2147)+Yb6/2cJ3670/]14KW� �54�+2107HLQ-:9;KN+^_� / � #@) ( � !'. 6 � 7 � . � ��10KW5N+�c2MGAQ74-��G5N+�FB9;-4LQKN+JAQ7np!c2+J7P/J5N/JUP+JAi7xo=10MGA c2MGAQ70+JAi3µ+2107e+Yb6/2cJ3670/�FB9;-<6/Yj�9;367x_

� � / � #@) )( 6�� .(!��! � .$#$.�� 5�� 54 � � �I� �54"+2147s36AE+�+YbRF6-0+21014KNMGA � � !¼OQ36K�<6MGK87hF6-0MQ<R36K8-0+a36AE+58KN1470+Z<6+ZA,+f3E<61|pPc��B9GcJ36A[<6+21:Oi3E+J5N1H5N+Zc2MGAQ70+JAi3�<6+f5?> K8AE1474-43EcJ74KNMGA[+2107|9;F6F658KNOi3E/^_ �� £Q¥�� w£A�CB 2=MGKNcJK�36A!+YbR+JUgF65N+�74K8-0/a<R3[58K8LQ-0+�<6+ �[KNc��B9;-0<� �[KNc � ��³_�?.MGAE14KN<6/J-0MGAE1h36A!<6MQcJ36UP+JAQ79Gc2cJ36Ua365d9;AQ7g5N+PAEMGUP1xoI9G<R-0+21010+21�+J7aAi36UP/J-0M^1e<6+n70/J5N/JF"�EMGAE+�+J7�70/J5N/2c2MGF6KN+m<6+nFS+J-01:MGA6AE+21a74-:9xLG9;K8585d9;AQ7<E9;AE1H36AE+]+JAQ74-0+JF6-4KN10+n�� / 2 # �". 6 �57 ( +(�� & � � . + ��( �87�+ �(��01 � � � � � F � � � � �&� ! + � !(#�( + . � � � . � � � �

�� -:9;AE1«jlMG-4Un9;74KNMGAE1h<6+Z<6MqcJ36UP+JAi701 � �!*� �� +�� :! 6�� . � �� + �:! 6 � . � ( 4 . 6 � ( +$+ . � - �� + 4 . 6 � ( +$+ . ( + ( 2 � 4(6 . + ( 2 � + * 6 .$!�* - �� + + ( 2 ( � �� + � - �� + 4$6 . + ( 2 ( � � � �� + � - �� + + * 6 .$!�* ( �#( 254 ! �G+ 7 . � ! �$6 . � � . � + * 6 .$!�* �3+ + 6 �� .$#(. 4 !%( + . � � .(#$.��( 4 7 . - �� + �#( 2'4 ! �G+87 . ( � � � �� + � - �� + ! �G6 . � � . ( 6 *". � + + 6 � � 4 ( �&�� ( � . � � 7 #$#$. � 4 ! � � - �� + 6 *'. ( � �� + � - �� + + + 6 ( � �� + � - �� + 4 ( �&�� #( � . ( � � � �� + � - �� + � 7 #(#$. ( � �� + � - �� + 4 ! � � ( � � � �� + � - �� + + * 6 .$!�* �3+ + 6 ( � �� + � - �� + � .$#(. 4 !�( + . ( � � � �� + � - �� + � .$#(.��( 487 . ( � � � �� + � - �

� �� 0! 6�� . �� 4 . 6 � ( +$+ . �� + ( 2 � � * 4 ( + � �� + ( 2 � � 4$6 . + ( 2 �� .$! + �� 4$6 . + ( 2 �� + * 6 .$!�* �� #( 2'4 ! �G+87 . �"1 �� 1 � �� ( 2'4 ! �$+87 . �� ! �G6 . � � . �� 6 *'. � ��(�* � . � . � * � 7 ((#$. � �� 6 *". �� + + 6 � �� + + 6 �� 4 ( �&�� ( � . �� F � � �� 4 ( �� #( � . �� 7 #(#$. � � ( 4 ! 7 ! � +�� 7�4 ((# 7 � �� 7 #$#$. �� 4 ! � ��$6 ! + �:. �� 4 ! � ��

�� ! �$6 . � � . �� + * 6 .$!�* �3+ + 6 � � F � � �� + * 6 .$!#* �3+ + 6 �� .$#(. 4 !�( + . �G� D$D & E-& �GD)� F<& � � �� .$#(. 4 !%( + . �� .$#(.��( 487 . �G� D$D & E-& �GD)� F<& � �� .$#(.��#( 487 . �

�� + * 6 .(!#* �� 4 . 6 � ( +(+ . �� 4 . 6 � ( +$+ . �� + ( 2 � � 7 ��!'! 6)� �� + ( 2 � � 4$6 . + ( 2 � �'#(! 7�+ �� 4$6 . + ( 2 �� + * 6 .$!�* �� #( 2'4 ! �G+87 . �"1 �� 1 � �� ( 2'4 ! �$+87 . �� ! �G6 . � � . �� 6 *'. � ��( 2 ! 7�+ . � .%($##* �:.(!#* �� 6 *'. �� + + 6 �� F �� + + 6 �� 4 ( �&�� ( � . �� F D �� 4 ( �� #( � . �� 7 #(#$. � . � !". ��+ ! � � . � .0/ �� 7 #$#$. �� 4 ! � ��$6 ! + �:. �� 4 ! � ��

�� ! �$6 . � � . �� + * 6 .$!�* �3+ + 6 � D � � �� + * 6 .$!#* �3+ + 6 �� .$#(. 4 !�( + . �G� D$D & � & D � �GD & � � �� .$#(. 4 !%( + . �� .$#(.��( 487 . �G� D$D & � & D � �GD & F � � E �� .$#(.��#( 487 . �

�� + * 6 .(!#* �� 4 . 6 � ( +(+ . �

� _��]*,+f5d9;A6ti9;tT+�<6+f74-:9;AE1«j�MG-4Un9;74KNMGA � � * � �

�� :! 6 � . ��

�sAP10MG3"�B9;K870+HF6-0Mq<R36K8-0+H<6+J3RbeF6-0/210+JAi7:9;74KNMGAE1.<RK =}/J-0+JAQ70+21`<6+Hc2+H<6MqcJ36UP+JAi7x_T*�9fF6-0+JUgKN´J-0+HF6-0/210+JAQ7:9;74KNMGA+2147]36A�9;A6Ai3B9;K8-0+m70/J5N/JF"�EMGA6KNOi3E+mcJ5d9G1014KNOQ3E+P<6+21474K8AE/mp�VJ74-0+gK8UgF6-4K8UP/m1036-]FB9;F6KN+J-a+J7�OQ36K`c2MGUgF}MG-470+J-:970MG3670+21Z5N+21ZK8ARj�MG-4Un9;74KNMGAE1ac2MGA6AQ3E+21a1436-]c�B9GcJ36AE+P<6+21ZF}+J-010MGA6AE+21x_D*�9�1:+2c2MGAE<6+gF6-0/210+JAi7:9;74KNMGA�+2147f36AE+58KN1470+m<6+PAEMGUP1e92LT+2c�c2MGUgFB9;t^A6KN+21xo�AQ36UP/J-0M^1e<6+P70/J5N/JF"�EMGAE+�+J7�<6+n70/J5N/2c2MGF6KN+m<6+21474K8AE/2+mF658367��G7�p¶VJ74-0+c2MGAE14365870/2+�+JA�58K8t^AE+]LqKd9e36A�AB9xLQK8ti9;70+J36-hK8Ai70+J-4AE+J7x_ ?.+J7s+Yb6+JUgF65N+ZK858583E1474-0+a<6MGAEcaF6583E14KN+J36-01)3674K858KN1�9;74KNMGAE1<D> 36A�UPVJUP+]<6MqcJ36UP+JAi7h<6+f\B9G10+^_�MG36-sF6-0MQ<R36K8-0+Z5d9�F6-0+JUgKN´J-0+aF6-0/210+JAi7:9;74KNMGA,o�MGA�3674K858KN10+Z5d9�74-:9;AE14jlMG-4Un9;74KNMGA!1436K8LG9;AQ70+P�� / 2 # �". 6 �57 ( +(�� & � � . + ��( �87�+ �(� � 1 � � � � � F � � � � �&� ! + � !(#�( + . � � � . � � � �� / � #@) �� #$. � !".$. � �". 6 �57 ( +(�� & � �/ 2 # + � ) / � # �� ! ��(4 ) �� & � D & ( 6 � � �� +(6 ! + � �( 6G2 � �� / � #@) (#* �$4 * � 2 . � !�( �$�� ! �G2 # �

� (�� (4 . ��4 * + # 7 � � �� D � �� + �� + � E & � +(6 ! + �(7��87 ( + !(# �� 7�+ � . + �(�� . � � . + ��( �87�+ �(��01 � � � � � F � � � �( 2�7�� / 2 # � � .��:#(! 6 ! �87 ( +5�� + ( � � �

� � � � �$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(� � �� / � #@) � . 254 #(! � . 2 ! � � ! � � � � �� + � �� +81�+ � � � +$+ *'! 7 6 . �� # �04 !�( +87 � *'. �� +81 + � �� + � ! � �$4 � . � * 7 � �� ( +�� . +�� +��(4 . � ��( +�� . + �(�� .0/ � � ! �G2 #�� !'! 6 � . �(� 1 � � � �� F � � � � � ��

� / � #@) ! 4$4 # � � � . 254 #$! � . � � ��

��

�� + � �� / � #<) � . 254 #$! � . �� $�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(� � �� / � #@) � . 254 #(! � . 2 ! � � ! � � 4 . 6 � ( +(+ . � �� 4 �� / � #@) ! 4$4 # � � � . 254 #$! � . � � .(#$.�� (� � 4$6 . + ( 2 � � �� / � #@) � .:/ � � �� / � #@) � .:/ � �� / � #@) ! 4$4 # � � � . 254 #$! � . � � .(#$.�� (� � + ( 2 � � �� + 6 � �� / � #@) ! 4$4 # � � � . 254 #$! � . � � .(#$.�� (� � + * 6 .(!#* � � �� 4 �

�� / � #<) � . 254 #$! � . �� $�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(� � �� / � #@) � . 254 #(! � . 2 ! � � ! � � + ( 2 � �� + � � / � #@) �'!(##*'. � (� � .$#(.�� 5��A& � � � �� + �

�� / � #<) � . 254 #$! � . �� $�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(� � �� / � #@) � . 254 #(! � . 2 ! � � ! � � 4(6 . + ( 2 � �� / � #@) �'!$#�*'. � (� � .$#$.�� 5��& � � �

�� / � #<) � . 254 #$! � . �

�0� -:9;AE1«jlMG-4Un9;74KNMGAE1h<6+Z<6MqcJ36UP+JAi701 � �!*� � � � �$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(� � �� / � #@) � . 254 #(! � . 2 ! � � ! � � + * 6 .(!#* � �� / � #@) ! 4$4 # � � � . 254 #$! � . � � �

�� / � #<) � . 254 #$! � . �� $�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(� � �� / � #@) � . 254 #(! � . 2 ! � � ! � � ��( 254 ! �$+87 . � �� / � #@) �'!$#�*'. � (� � .$#$.�� 5��& � � � � + 6 � �

�� / � #<) � . 254 #$! � . �� $�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(� � �� / � #@) � . 254 #(! � . 2 ! � � ! � � ! �G6 . � � . � �� / � #@) ! 4$4 # � � � . 254 #$! � . � � �

�� / � #<) � . 254 #$! � . �� $�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(� � �� / � #@) � . 254 #(! � . 2 ! � � ! � � 6 *'. � �� / � #@) �'!$#�*'. � (� � .$#$.�� 5��& � � � � + 6 � �

�� / � #<) � . 254 #$! � . �� $�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(� � �� / � #@) � . 254 #(! � . 2 ! � � ! � � + + 6 � �� / � #@) 7 � . ��(� � �&�$687 + �� #$. + �� ! ( - � � � �� / � #@) �"!$#�*'. � (� � .(#$.�� (� ��& � � � � + 6 � �� / � #<) 7 �

�� / � #<) � . 254 #$! � . �� $�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(� � �� / � #@) � . 254 #(! � . 2 ! � � ! � � 4 ( �� ( � . � �� / � #@) �'!$#�*'. � (� � .$#$.�� 5��& � � � �

/ � #<) � .:/ � � �� / � #<) � .0/ � �� / � #<) � . 254 #$! � . �� $�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(� � �� / � #@) � . 254 #(! � . 2 ! � � ! � � � 7 #$#(. � �� / � #@) �'!$#�*'. � (� � .$#$.�� 5��& � � � �

/ � #<) � .:/ � � �� / � #<) � .0/ � �� / � #<) � . 254 #$! � . �� $�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(� � �� / � #@) � . 254 #(! � . 2 ! � � ! � � 4 ! � � � �� / � #@) �'!$#�*'. � (� � .$#$.�� 5��& � � � � + 6 � �

�� / � #<) � . 254 #$! � . �� $�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(� � �� / � #@) � . 254 #(! � . 2 ! � � ! � � + * 6 .(!#* �3+ + 6 � �� . 2 � + * 6 .(!#* + ◦ ) �� . 2 � � / � #@) �"!$#�*'. � (� � .(#$.�� (� ��& � � � � + 6 � �

�� / � #<) � . 254 #$! � . �� $�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(� � �� / � #@) � . 254 #(! � . 2 ! � � ! � � � .$#$. 4 !%( + . � �� . 2 �#�%� # �04 !%( + .*) �� . 2 � � / � #<) �'!(##*". � (� � .$#(.�� 5��A& � � � � + 6 � �

�� / � #<) � . 254 #$! � . �� $�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(� � �� / � #@) � . 254 #(! � . 2 ! � � ! � � � .$#$.��#( 487 . � �� . 2 �#�%� # � �#( 487 .*) �� . 2 � � / � #<) �'!(##*". � (� � .$#(.�� 5��A& � � �

�� / � #<) � . 254 #$! � . �� $�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(� � �� / � #<) �&�� #(. � !'.$. � �

� _��]*,+f5d9;A6ti9;tT+�<6+f74-:9;AE1«j�MG-4Un9;74KNMGA � � * ��

*=>�/J5N/JUP+JAQ7 / � #<) (#* �$4 * � K8AE<RKNOi3E+mOi3E+n5N+P<6MQcJ36UP+JAQ7�cJK8\65N+m+2147a36A�<6MQcJ36UP+JAQ7 ! �!* <6MGAi7�5N+P7ÏÎQF}++2147n<6MGA6AE/�FB9;-P36AE+�-0/Yj�/J-0+JAEc2+�F636\658KNOQ3E+^_`*,+21�9;3674-0+21m9;7474-4K8\636701mK8AE<RKNOi3E+JAQ7mOQ3E+�5?> K8AE<6+JAi7:9;74KNMGA <6+21/J5N/JUP+JAi701�<6MGK87mVJ74-0+�F6-0/210+J-4LT/2+ôÒQ3E+�5?>�+JAEc2Mq<E9;tT+¶+2147nÍ � � *�9;74K8A �[+J7nOQ3E+�5N+�<6MqcJ36UP+JAi7�cJK8\65N+�<6MGK87K8AEcJ5836-0+Z70MG3670+21|5N+21)<6/2cJ5d9;-:9;74KNMGAE1 � �!*=_�s3674-0+f5d9�F6-0+JUgKN´J-0+Z-0´Jt^5N+ô6<6MGAi7)5N+s�E5874-0+

� � �1y>@9;F6FB9;-4KN+fFB9;-)<6/Y�EA6K874KNMGA[p�5d9�-:9GcJK8AE+]<R3�<6MQcJ36UP+JAQ710MG36-0c2+ô25N+21D�E5874-0+21�c2MGAi74KN+JA6AE+JAQ7I10K8UgF65N+JUP+JAi7�5N+=AEMGUÃ<6+21,/J5N/JUP+JAi701�9;3Rb6Oi3E+J5N1D5d9H-0´Jt^5N+=<6MGK87�1x>@9;F6F658KNOQ3E+J-x_*�9|j�MG-4UP+.<6+.5d9|F6-0+JUgKN´J-0+C-0´Jt^5N+CK8AEcJ58367�<E9;AE1�5N+W<6MqcJ36UP+JAi7=cJK8\65N+^_^¬sAe9;F6F}+J5Ep / � #<) ! 4(4 # �� . 2'4 #$! � . �9;F6F658KNOQ3E+Z-0/2cJ36-014K8LT+JUP+JAi7h5N+21H-0´Jt^5N+21|9;3Rb��E5N1)<6+f5d9g-:9GcJK8AE+^_

*�9�-0´Jt^5N+s1436-.5N+21C/J5N/JUP+JAi701)<6+sAEMGU 4 . 6 � ( +$+ .�3674K858KN10+|5?> K8AE1074-43EcJ74KNMGA / � #<) � .:/ � F}MG36-CF6-0MQ<R36K8-0+h36A70+YbR70+gc2MGAi74-��G5N/P+YbRF658KNcJK870+JUP+JAi7�FB9;-Z5N+�j�9;K87ZOQ3,>�MGA~<6MGK87]-0+JF6-0MQ<R36K8-0+g+YbE9GcJ70+JUP+JAi7�70MG367Z5N+gc2MGAi70+JAQ3�<6+c2+J7s/J5N/JUP+JAQ7PuwKNcJK�36A!cx9;-:9GcJ70´J-0+�+210FB9Gc2+yzY_�*=> 3674K858KN1�9;74KNMGA!<D>@9;F6F}+J5N1Zp / � #@) ! 4$4 # � � � . 254 #$! � . � 92LT+2c�36A10/J5N+2cJ70+J36-�FB9;-474KNcJ3658KN+J-.c2MGAi74-��G5N+H5?>�MG-0<R-0+)<E9;AE1�5N+2OQ3E+J565N+21I�E5N1�LTMGAQ7`VJ74-0+C74-:9;K870/21=+J7�FS+J-4UP+J7W<D> K8AE10/J-0+J-=<6+21j�MG-4UP+21spgtT/JAE/J-0+J-h+JAi74-0+�5N+21)-0/21436587:9;701h1436-)5N+21)�E5N1x_B*`> K8AE1474-43EcJ74KNMGA / � #<) �'!(##*". � (� �9xLT+2c]36A!10/J5N+2cJ70+J36-/Jti9;5Ipg36A¶F}MGK8Ai7s1y>@9;F6F658KNOi3E+�9;3¶A,+f3E<¶c2MG36-:9;AQ7|�E5874-0/�FB9;-)5d9P-0´Jt^5N+^_B*=> 3674K858KN1:9;74KNMGA�<D> 36AE+�K8AE1474-43EcJ74KNMGA/ � #@) 7 "<E9;AE1n5d9�-0´Jt^5N+�1x>@9;F6F658KNOQ3B9;Ai7�9;3Rb /J5N/JUP+JAQ701 + + 6 FS+J-4UP+J7m<6+�AE+�tT/JAE/J-0+J-n36A 70+YbR70+�OQ3E+�14Kc2+J7g/J5N/JUP+JAi7P<E9;AE1e5N+�<6MQcJ36UP+JAQ7P10MG36-0c2+�A,>�+2147eFB9G1�LQKN<6+ ��MGA�LTMGK87�KNcJKC5?> 3674K858KN1:9;74KNMGA <D> 36AE+mj�MGAEcJ74KNMGAF6-0/2<6/Y�EA6KN+ �&�$6 7�+ �� #(. + �� !�1x>@9;F6F658KNOi3B9;AQ7s9;3¶c2MGAQ70+JAi3�<6+f5?>�/J5N/JUP+JAi7sc2MG36-:9;AQ7x_*�9h74-:9;AE1«j�MG-4Un9;74KNMGAn1436K8L^9;Ai70+HF6-0Mq<R36K87�36Ag7:9;\65N+x9;3 ! �[*¶9xLT+2cH36A6KNOQ3E+JUP+JAi7=5N+21�AEMGUP1yoGF6-0/JAEMGUP1xo5d9ec2MGUgFB9;tÂ6KN+a+J7|5N+21HAi36UP/J-0M^1h<6+f70/J5N/JF"�EMGAE+a+J7)<6+Z70/J5N/2c2MGF6KN+m�� / 2 # �". 6 �57 ( +(�� & � � . + ��( �87�+ �(� � 1 � � � � � F � � � � �&� ! + � !(#�( + . � � � . � � � �� / � #@) �� #$. � !".$. � �". 6 �57 ( +(�� & � �/ 2 # + � ) / � # �� ! ��(4 ) �� & � D & ( 6 � � �� +(6 ! + � �( 6G2 � �� / � #@) (#* �$4 * � 2 . � !�( �$�� ! �G2 # �

� (�� (4 . ��4 * + # 7 � � �� D � �� + �� + � E & � +(6 ! + �(7��87 ( + !(# �� 7�+ � . + �(�� . � � . + ��( �87�+ �(��01 � � � � � F � � � �( 2�7�� / 2 # � � .��:#(! 6 ! �87 ( +5�� + ( � � �

� � � � �$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(� � �� / � #@) � . 254 #(! � . 2 ! � � ! � � � � �� + � �� +81�+ � � � +$+ *'! 7 6 . �#( 254 #$. � �� +81 + � �� + � ! � �$4 � . � * 7 � �� ( +�� . +�� +��(4 . � ��( +�� . + �(�� .0/ � � ! �G2 #�� !'! 6 � . �(� 1 � � � �� F � � � � � ��

� � ! + #(. + ( 6)� . 65�� $6 �� 6��:+ ( 2 �� )� �� %( 2 �� )� �� ( 254 ! �$+87 . �� #+%� # �04 !%( + . �� #+%� # � �#( 487 . �� (6 �� / � #@) ! 4$4 # � � � . 254 #$! � . � � �� ! + #$. ��

��

�� + � �

� �� -:9;AE1«jlMG-4Un9;74KNMGAE1h<6+Z<6MqcJ36UP+JAi701 � �!*�� / � #<) � . 254 #$! � . �� $�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(� � �� / � #@) � . 254 #(! � . 2 ! � � ! � � 4 . 6 � ( +(+ . � �� $6 �� / � #@) ! 4$4 # � � � . 254 #$! � . � � .(#$.�� (� � 4$6 . + ( 2 � � �� / � #@) ! 4$4 # � � � . 254 #$! � . � � .(#$.�� (� � + ( 2 � � �� / � #@) ! 4$4 # � � � . 254 #$! � . � � .(#$.�� (� � + * 6 .(!#* � � �� (6 �

�� / � #<) � . 254 #$! � . �� $�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(� � �� / � #@) � . 254 #(! � . 2 ! � � ! � � + ( 2 � �� / � #<) �"!$##*". � (� � .$#(.�� (��A& � � � ��

�� / � #<) � . 254 #$! � . �� $�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(� � �� / � #@) � . 254 #(! � . 2 ! � � ! � � 4(6 . + ( 2 � �� / � #<) �"!$##*". � (� � .$#(.�� (��A& � � � ��

�� / � #<) � . 254 #$! � . �� $�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(� � �� / � #@) � . 254 #(! � . 2 ! � � ! � � + * 6 .(!#* � �� / � #@) ! 4$4 # � � � . 254 #$! � . � � �� / � #<) � . 254 #$! � . �

� � � � �$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(� � �� / � #@) � . 254 #(! � . 2 ! � � ! � � ��( 254 ! �$+87 . � �� / � #<) �"!$##*". � (� � .$#(.�� (��A& � � � ��

�� / � #<) � . 254 #$! � . �� $�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(� � �� / � #@) � . 254 #(! � . 2 ! � � ! � � ! �G6 . � � . � �� / � #<) � . 254 #$! � . �� $�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(� � �� / � #@) � . 254 #(! � . 2 ! � � ! � � + * 6 .(!#* �3+ + 6 � �� / � #<) � . 254 #$! � . �� $�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(� � �� / � #@) � . 254 #(! � . 2 ! � � ! � � � .$#$. 4 !%( + . � �� / � #<) �"!$##*". � (� � .$#(.�� (��A& � � � ��

�� / � #<) � . 254 #$! � . �� $�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(� � �� / � #@) � . 254 #(! � . 2 ! � � ! � � � .$#$.��#( 487 . � �� / � #<) �"!$##*". � (� � .$#(.�� (��A& � � � ��

�� / � #<) � . 254 #$! � . �� $�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(� � �� / � #<) �&�� #(. � !'.$. � �

?.+J7470+H10+2c2MGAE<6+H74-:9;AE14jlMG-4Un9;74KNMGAP-0+21:10+JUa\65N+)ph5d9sF6-0+JUgKN´J-0+^oiph5d9fcJ-0/x9;74KNMGAn<R3e7:9;\65N+x9;3n+JA ! �!*�F6-0´21x_�583E14KN+J36-01�-0´Jt^5N+21eMGAi7�36AE+njlMG-4UP+nLQKN<6+ �Ic2+2cJKWF}+J-4UP+J7e<D>�/JLQK870+J-�5N+P74-:9;K870+JUP+JAQ7gFB9;-�<6/Yj?9;367e9;F6F658KNOQ3E/FB9;- � � *�10+J5NMGA�5N+21W<6+J3Rbm-0´Jt^5N+21WLq3E+21WF6-0/2c2/2<6+JUgUP+JAi7x_ � 9;AE1.5N+21`-0´Jt^5N+21Hp]jlMG-4UP+sLqKN<6+^oi36A�/J5N/JUP+JAi7)<6+c2MGAi70+JAQ3¶7ÏÎQF}+ � � � �� + �mLT+J-4-:9;K87|c2+]c2MGAQ70+JAi3[c2MGF6KN/a<E9;AE1)5N+Z<6MqcJ36UP+JAi7scJK8\65N+^_ 2

� _�� 1 -:9;UgUn9;K8-0+21h9;7474-4K8\63E/2+21|+J7)74-:9;AE14jlMG-4Un9;74KNMGAE1 � � �

� ¸ � ��Ä}É � � É)¿0ÄSÆ�Á&ÉHÀEÀBÄ}¿��»�Æ�Á&ÆIÀÈÀBÄ}É)¾�Á��HÄ�� ÉCÀ�¿ �)¾�Á(sMG3E1f92LTMGAE1f<6/ �0pej?9;K87|5N+]FB9;-:9;585N´J5N+�+JAi74-0+�t^-:9;UgUn9;K8-0+�AEMGARX³c2MGAi70+YbR743E+J585N+g+J7s� �e_�ÍÏ5,FB9;-:9��N7h70MG3679;3E1014KBK8Ai70/J-0+2101:9;AQ7W<6+)j�9;K8-0+H36AnFB9;-:9;585N´J5N+|+JAi74-0+s5N+21�74-:9;AE1«j�MG-4Un9;74KNMGAE1 � � * +J7`5N+21=-0´Jt^5N+21`1:/JUn9;Ai74KNOQ3E+21<6+21Ht^-:9;UgUn9;K8-0+21f9;7474-4K8\63E/2+21x_ ;�A[Oi3E+J5NOQ3E+]10MG-470+ôRK85�+2107H70+JAi7:9;Ai7h<D>�/2cJ-4K8-0+n�

� ��%74-:9;AE14jlMG-4Un9;74KNMGA � � *�� 1 -:9;UgUn9;K8-0+a9;7474-4K8\63E/2+

;�Aµ+>=D+J7xo=36AE+¶74-:9;AE1«jlMG-4Un9;74KNMGA � � *ÃF}+J-4UP+J7m<6+¶74-:9;K870+J-m5N+21nA,+f3E<61m<D> 36A 10MG3E1«XÏ9;-4\6-0+�70MG367�+JAK8AE10/J-:9;AQ7|<6+21)9GcJ74KNMGAE1)10/JUn9;AQ74KNOi3E+21)+JAQ74-0+Zc2+J3RbQX³cJK?_8�sA¶9�<6MGAEcf36AE+]9;AB9;5NMGt^KN+Z+JAQ74-0+Z74-:9;AE1«j�MG-4Un9;74KNMGAE1� � *"+J7Ht^-:9;UgUn9;K8-0+21h*}XÏ9;7474-4K8\63E/2+21x_�?.+JF}+JAE<E9;Ai7xoBK85,+YbqKN1070+fF6583E14KN+J36-01)-0+21474-4KNcJ74KNMGAE1hpgc2+J7470+]/2OQ3B9;74KNMGA,_��>@9;\}MG-0<DoTK85Ej�9;367.c2MGUgF6-0+JAE<R-0+sOQ3E+ � � *¶+2147=36AE+|5d9;A6ti9;tT+|<D>@9GcJ74KNMGAE1.10/JUn9;Ai74KNOQ3E+21.\S+x9;3Ec2MG36FmF6583E1F636KN101:9;AQ7WOQ3E+C5N+21=t^-:9;UgUn9;K8-0+21.*}XÏ9;7474-4K8\63E/2+21WFB9;-`5N+.j?9;K87Òi3E+)5?>�MGAPFS+J367.9G<R-0+21010+J-`<E9;AE1`36AE+H-0´Jt^5N+ � � *AEMGA¶10+J365N+JUP+JAQ7|5N+ZA,+f3E<[c2MG36-:9;Ai7eulc^>�+2147«XÏp±X³<RK8-0+ac2MG-4-0+214F}MGAE<E9;Ai7Z9;3�AEMGARX?70+J-4UgK8AB9;5�+JA�FB9;-474KN+Zti9;3Ec�E+<6+s5d9]-0´Jt^5N+yzW+J7.5N+21À,+f3E<61W�E5N1Zulc^>�+2147«XÏp±X³<RK8-0+fc2MG-4-0+214F}MGAE<E9;Ai7|9;3Rbm14ÎqUa\}MG5N+21.<6+|5d9aFB9;-474KN+f<R-0MGK870+h<6+s5d9F6-0Mq<R3EcJ74KNMGA�zHUn9;KN1s+JA¶tT/JAE/J-:9;5�70MG367f9;3674-0+]A,+f3E<!<E9;AE1)5?>@9;-4\6-0+�<R3¶<6MqcJ36UP+JAi7x_��WKN+JA!+JAi70+JAE<R3,oSc2+J7470+F}M^1014K8\6K858K870/|9h36AP-0+JLT+J-01yoTOi36KE+2107=5?>�MG\658K8ti9;74KNMGAm<6+HUn9;K8AQ70+JA6K8-`70MG367=5?>@9;-4\6-0+s<R3n<6MqcJ36UP+JAi7.9Gc2c2+21:14K8\65N+)+JAUP/JUPMGK8-0+PF}+JAE<E9;Ai7�70MG3670+g5d9�74-:9;AE1«j�MG-4Un9;74KNMGA,_�*�+21]t^-:9;UgUn9;K8-0+21e9;7474-4K8\63E/2+21aMG\E10+J-4LT+JAQ7a36A~F6-4K8AEcJK8F}+<6+�5NMQcx9;58K870/�<E9;AE1s5N+21s-0´Jt^5N+21f10/JUn9;Ai74KNOQ3E+21fOi36K�FS+J-4UP+J7xoSc2MGUgUP+�AEMG3E1s5?>@9xLTMGAE1hLQ3,o�<6+aFB9;-0c2MG36-4K8-h36AE+10+J365N+hj�MGKN1H5?>@9;-4\6-0+a<6+Z<6/J-4K8L^9;74KNMGA,oELTMGK8-0+a<6+fAE+ZUPVJUP+ZFB9G1H5N+Zc2MGAE1474-436K8-0+^_�!9;58t^-0/gc2+J5d9Ro}5N+21Z74-:9;AE14jlMG-4Un9;74KNMGAE1 � � * 10MGAQ7a9;3E1014K�58K8UgK870/2+21ZFB9;-Z-:9;F6F}MG-47a9;3Rb�t^-:9;UgUn9;K8-0+21�9;7«X74-4K8\63E/2+21x_";�A�+>=D+J7xoq36AE+f74-:9;AE1«j�MG-4Un9;74KNMGA � � *�AE+hF}+J367CFB9G1CUPMQ<RKk�B+J-H5?>@9;-4\6-0+Z10MG36-0c2+Z<6+h5d9�74-:9;AE1«j�MG-«XUn9;74KNMGA,_IÍ³5`+2107]FSM^1:14K8\65N+n+JA � � * <6+g-0/2cJ36F}/J-0+J-�<6+21�FSMG-474KNMGAE1�<6/ �4p�tT/JAE/J-0/2+21e<6+g5?>@9;-4\6-0+mcJK8\65N+ô�FB9;-5N+]UP/2cx9;A6KN10UP+�<6+21sLG9;-4Kd9;\65N+21h+J7f<6+21)FB9;-:9;UP´J74-0+21x_A?.+JF}+JAE<E9;Ai7xo}c2+21 'Y®«�yG�n�Y�B�w� � � �G®x¯Y®0�eMGAi7h36A¶7ÏÎQF}+14F}/2cJKk�BOi3E+H<RK =D/J-0+JAi7.<R3g7³ÎqFS+H<6MqcJ36UP+JAi7 � �!*=_0;�AnF6-:9;74KNOi3E+ôTc2+J5d9hLT+J367W<RK8-0+)Oi3,>�MGAgAE+CF}+J367=F6-0+210OQ3E+-4KN+JA�j?9;K8-0+f9xLT+2cf36A�jw-:9;tÛP+JAQ7)<D>@9;-4\6-0+ôEc2+h7³ÎqFS+f/J7:9;Ai7H70MG7:9;5N+JUP+JAQ7|MGFB9GOQ3E+^_6*�9�F6-4K8AEcJK8FB9;5N+Zc��EM^10+ZOQ3E+5?>�MGA�FS+J367aj�9;K8-0+�+2147�<6+m5N+nc2MGF6KN+J-e<E9;AE1�5N+n<6MqcJ36UP+JAi7gcJK8\65N+^_@�sA�3674K858KN10+�c2+J7470+mFSM^1010K8\658K870/P5NMG-010OQ3,>�MGALT+J367�tT/JAE/J-0+J-�36AE+H10+J365N+Wj�MGKN1�36Aejw-:9;tÛP+JAQ7=<D>@9;-4\6-0+CUn9;KN1�5?> K8AE10/J-0+J-�F6583E14KN+J36-01Ij�MGKN1�<E9;AE1�5?>@9;-4\}MG-0+210c2+JAEc2+cJK8\65N+^_*�9ac2MGAE1:/2Oi3E+JAEc2+s<6+|5d9]-0+21474-4KNcJ74KNMGA�<D> � � *�pZAE+)FB9G1WUPMq<RKk�B+J-W5N+21C9;-4\6-0+21W+J7CpZAE+|FSMG36LTMGK8-H9Gc2c2/2<6+J-9;3 c2MGAi70+JAQ3 <6+21�jw-:9;tÛP+JAQ701P<D>@9;-4\6-0+21P+2147eOi3,>�MGA AE+�F}+J367e+JA 36AE+�10+J365N+�FB9G1010+�<6+�74-:9;AE1«j�MG-4Un9;74KNMGAcx9;5NcJ365N+J-�5?>�/2Oi36K8L^9;5N+JAi7e<D>@9;7474-4K8\636701g14ÎqAi7��E/J74KN10/21�MG3 �E/J-4K870/21�1436-a36A�<6MQcJ36UP+JAQ7 � �!*=_ IMG36-�-0/x9;58KN10+J-5?>�/2OQ36K8LG9;5N+JAQ7|<D> 36A�cx9;5NcJ365,<D>@9;7474-4K8\636701xo6K85Sj?9;367)1x>�+JA�-0+JUP+J7474-0+ap�36A¶9;3674-0+ZMG3674K85,<6+sUn9;A6K8F6365d9;74KNMGA!<6+219;-4\6-0+21|<6+Z<6MqcJ36UP+JAi701 � �[* �R5?> � =Í.�� OQ3E+fAEMG3E1HLT+J-4-0MGAE1hpe5d9e10+2cJ74KNMGA � _ �R_*�9ac2MGAEcJ583E10KNMGA�<6+21C<6+J3RbP-0+JUn9;-0OQ3E+21CF6-0/2c2/2<6+JAi70+21H+2147COQ3,> 36AE+|74-:9;AE1«j�MG-4Un9;74KNMGA � � *òqpac2MGAE<RK874KNMGA<6+)-0+210FS+2cJ70+J-=5N+|F6-4K8AEcJK8FS+s<6+)5NMqcx9;58K870/|<6+21`-0´Jt^5N+21W10/JUn9;AQ74KNOi3E+21.+J7W<6+)AE+Hj?9;K8-0+|OQ3,> 36AE+H74-:9;AE1«j�MG-4Un9;74KNMGA<D> 36A&9;-4\6-0+�10MG36-0c2+[+JA 36A&9;-4\6-0+�cJK8\65N+ô`F}+J367�VJ74-0+¶Lq3E+[c2MGUgUP+!36AÈ10c�E/JUn9�<6+[74-:9G<R3EcJ74KNMGA,_H�f+219;F6F658KNcx9;74KNMGAE1fcJ5d9G1014KNOQ3E+21s<6+21h10c�E/JUn9G1h<6+a74-:9G<R3EcJ74KNMGA�c2MGUgUP+a5d9nc2MGAE1474-43EcJ74KNMGA�<D> 36A!9;-4\6-0+e9;\E1474-:9;K87MG3�5d9m-0+YX³14ÎqAi7��E´210+P<D> 36A~1:MG36-0c2+�<6+eF6-0MGt^-:9;UgUP+mp�FB9;-474K8-]<D> 36A"9;-4\6-0+g<6+g<6/J-4K8LG9;74KNMGAµu 4S®4�J��l�GÐ 4�®��w�B�0z10MGAQ7]<6MGAEcej�9GcJK85N+JUP+JAQ7]-0/x9;58KN1:9;\65N+21aFB9;-Z36AE+e74-:9;AE1«jlMG-4Un9;74KNMGA � � *Ãu�p�c2+2cJK`F6-0´21ZOi3E+e5N+gc2MGAQ74-��G5N+g�EA<R3�j�MG-4Un9;7)<6+]10MG-474KN+]+2107HFB9;-«jlMGKN1)<6/J58KNcx9;7s+JA�� *IzY_?.MGAE14KN<6/J-0MGAE1f<D>@9;\SMG-0<¶5N+ZF6-0MG\65N´JUP+�<6+a5d9PcJ-0/x9;74KNMGA�<D> 36A!9;-4\6-0+�9;\E1474-:9;K87hpPFB9;-474K8-s<D> 36A!9;-4\6-0+�<6+<6/J-4K8L^9;74KNMGA,oB+J7)c2+fFB9;-)36A¶+Yb6+JUgF65N+]c2MGAEcJ-0+J7x_

�� £Q¥�� w£A�� 36F6FSM^1:MGAE1g36AE+�t^-:9;UgUn9;K8-0+¶c2MGAEcJ-0´J70+[<6+21P+YbRF6-0+21014KNMGAE1nOQ3E+�AEMG3E1n9xLTMGAE1m10MG36LT+JAQ7

� � � -:9;AE1«jlMG-4Un9;74KNMGAE1h<6+Z<6MqcJ36UP+JAi701 � �!*3674K858KN10/2+P�

E → E � T | T

T → T � F | F

F → ( E - | N | I

*�9g� ��c2MG-4-0+214F}MGAE<E9;Ai70+^o �#( + � 6 . � . &"�� o6MG\670+JAi3E+a1:+J5NMGA�5N+21H-0´Jt^5N+21|<6+f5d9g1:+2cJ74KNMGA � _ �� / 2 # �". 6 �57 ( +(�� & � � . + ��( �87�+ �(� � 1 � � � � � F � � � � � �� + � (�( � � � ##* � ��+ - * + - �� + + (�( + � �

( 7 � � � - * � - �� + � (�( 4 � � � � 4 � - * � * 1 - �� + � ( � � � �� + � - �� + 1 ( � � � �� + � - �� + � #�* � �� +�� + �

( 7 � �� +�� + 4 � �� + � �� + 4 � �� + � �

¬sAE+�t^-:9;UgUn9;K8-0+.9;\E1074-:9;K870+`143*)n1:9;AQ70+=F}MG36-�+YbRF6-4K8UP+J-�<6+�Un9;A6KN´J-0+./2OQ36K8LG9;5N+JAQ70+=5N+21,F"�6-:9G1:+21,-0+2c2MGA6Ai3E+21FB9;-)5d9�t^-:9;UgUn9;K8-0+aF6-0/2c2/2<6+JAi70+�+2147]�e → e � e | e � e | n | i

*�9g� ��c2MG-4-0+214F}MGAE<E9;Ai70+�+2147xo8! + ��(6 ! 7�� . &"� �)� �� / 2 # �". 6 �57 ( +(�� & � � . + ��( �87�+ �(� � 1 � � � � � F � � � � � �� + . (�( . � 4 ##* � � . - * ( . � �( 7 � � . - * + * 7 - �� + + ( � � � �� + � - �� + 7 ( � � � �� + � - �� + 4 #�* � �� +�� + )( 7 � �� +��

ÍÏ5`+2147aF}M^1014K8\65N+m<6+n<6/Y�EA6K8-�36AE+m<6/Y�EA6K874KNMGA <RK8-4K8tT/2+nFB9;-�5d9�14ÎqAi7:9±b6+P-0/x9;58KN1�9;Ai7�5d9�c2MGAE1474-43EcJ74KNMGA <D> 36A9;-4\6-0+[9;\E1074-:9;K87�p�FB9;-474K8-�<6+�5?>@9;-4\6-0+[<6+¶<6/J-4K8L^9;74KNMGA,_W*`>@9;7474-4K8\6367�14ÎqAi7��E/J74KN1:/ !~LG9~c2MGAi70+JA6K8-�5?>@9;-4\6-0+9;\E1474-:9;K87x_�-0Mq<R3EcJ74KNMGA %s´Jt^5N+Z10/JUn9;Ai74KNOQ3E+E → E1 � T E & !*) � � 6 .$. 6 ��((.#* � ( e � E1 & ! � � 6 .(. 6 ��($.�* � ( � - � T & ! -E → T E & ! ) � T & ! -T → T1 � F T & ! ) � � 6 .(. 6 ��($.�* � ( e � T1 & ! � � 6 .(. 6 �%($.�* � ( � - � F & ! -T → F T & !*) � F & ! -F → ( E - F & !*) � E & ! -F → N F & !*) � � 6 .(. 6 �%($.�* � ( e � � 6 .$. 6 ��((.#* � ( n � N & �'!$#(#$.0/ -�-F → I F & !*) � � 6 .(. 6 �%($.�* � ( e � � 6 .$. 6 ��((.#* � ( i � I & �'!(#$#$.0/ - -

*�9n74-:9;AE1«j�MG-4Un9;74KNMGA � � * 1436K8L^9;Ai70+�F6-0+JAE<¶36A�<6MQcJ36UP+JAQ7f-0+214FS+2cJ7:9;AQ7f5d9P� � ��( + � 6 . � . & � �)� +J7h5d974-:9;AE1«j�MG-4UP+P+JA�36A"<6MqcJ36UP+JAi7�10/JUn9;Ai74KNOQ3E+JUP+JAi7e/2Oi36K8L^9;5N+JAi7a-0+214FS+2cJ7:9;AQ7]5d9�� ! + ��$6 ! 7�� . & � �)� _

� _�� 1 -:9;UgUn9;K8-0+21h9;7474-4K8\63E/2+21|+J7)74-:9;AE14jlMG-4Un9;74KNMGAE1 � � �

;�585N+P+2107]MG\670+JAi3E+P<6+g5d9�<6/Y�EA6K874KNMGA�<RK8-4K8tT/2+gFB9;-Z5d9�14ÎqAi7:9±b6+P+JA�3674K858KN1:9;AQ7]5d9mjlMGAEcJ74KNMGA / � #<) .(#$. 2 . + �F}MG36-�cJ-0/2+J-�5N+21�A,+f3E<61�+J7�5d9.jlMGAEcJ74KNMGA / � #@) ! 4$4 # �� . 254 #(! � . � FSMG36-�cx9;5NcJ365N+J-�5N+21�L^9;5N+J36-01�<6+=5?>@9;7474-4K8\636714ÎqAi7��E/J74KN10/ !6_ �sA¶3674K858KN10+�<6+21s1474-43EcJ7436-0+21h<6+ac2MGAQ74-��G5N+ / � #<) ��!�(�( � .PFSMG36-s74-:9;K870+J-sK8AE<6/JF}+JAE<E9;UgUP+JAi75N+21f<RK =}/J-0+JAQ701f7³ÎqFS+21h<6+�A,+f3E<61Z<6+a5?>@9;-4\6-0+�<6+e<6/J-4K8LG9;74KNMGA ul<6MqcJ36UP+JAi7Z10MG36-0c2+yzs10+J5NMGA!5d9PF6-0Mq<R3EcJ74KNMGA9;F6F658KNOQ3E/2+^_�� / 2 # �". 6 �57 ( +(�� & � � . + ��( �87�+ �(� � 1 � � � � � F � � � � �&� ! + � !(#�( + . � � � . � � � �� / � #@) �� #$. � !".$. � �". 6 �57 ( +(�� & � �/ 2 # + � ) / � # �� ! ��(4 ) �� & � D & ( 6 � � �� +(6 ! + � �( 6G2 � �� / � #@) (#* �$4 * � 2 . � !�( �$�� / 2 # �

� (�� (4 . � �� . 2'� � ! + ��(6 ! 7�� . &"� �)��7�+ � . + �(�� . � � . + ��( �87�+ �(��01 � � � � � F � � � �( 2�7�� / 2 # � � .��:#(! 6 ! �87 ( +5�� + ( � � �� / � #@) 4$6 . � . 6 �". ��4 !��:.,.$#$. 2 . +�� :��:� � � �

� � � � �$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$� � �� / � #@) � . 254 #(! � . 2 ! � � ! � � � � �� / � #@) � !�( ( � . �� / � #@) �)!'. + � . �&�(�� ! 7 # � )$) � ##* � � �� / � #<) .(#$. 2 . + �,+ ! 2 . �� . � �� / � #<) ! 4(4 # �� . 2'4 #$! � . � � .$#$.�� 5�� / � #<) .$#(. 2 . +��,+ ! 2 . �� 4 ##* � � � �� / � #<) ! 4(4 # �� . 2'4 #$! � . � � .$#$.�� 5�� + � � �

�� / � #@) .$#$. 2 . +�� / � #@) � !". + �� / � #@) ( � !". 6 � 7 � . �� / � #<) ! 4$4 # �� . 2'4 #(! � . � � �

�� / � #@) ( � !'. 6 � 7 � . �� / � #<) � !%(�( � . �

�� / � #<) � . 254 #$! � . �� $�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$� � �� / � #@) � . 254 #(! � . 2 ! � � ! � � + � �� / � #@) � !�( ( � . �� / � #@) �)!'. + � . �&�(�� ! 7 # � )$) � ( 7 � � �� / � #<) .(#$. 2 . + �,+ ! 2 . �� . � �� / � #<) ! 4(4 # �� . 2'4 #$! � . � � .$#$.�� 5�� + � � �� / � #<) .$#(. 2 . +��,+ ! 2 . �� ( 7 � � � �� / � #<) ! 4(4 # �� . 2'4 #$! � . � � .$#$.�� 5��

�� / � #@) .$#$. 2 . +�� / � #@) � !". + �� / � #@) ( � !". 6 � 7 � . �� / � #<) ! 4$4 # �� . 2'4 #(! � . � � �

�� / � #@) ( � !'. 6 � 7 � . �� / � #<) � !%(�( � . �

�� / � #<) � . 254 #$! � . �� $�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$� � �� / � #@) � . 254 #(! � . 2 ! � � ! � � � � �� / � #@) � !�( ( � . �� / � #@) �)!'. + � . �&�(�� ! 7 # � )$) 4 �� / � #<) ! 4$4 # �� . 2'4 #(! � . � � .$#(.�� 5��

�� / � #@) � !". + �

� �� -:9;AE1«jlMG-4Un9;74KNMGAE1h<6+Z<6MqcJ36UP+JAi701 � �!*� / � #@) �)!'. + � . �&�(�� ! 7 # � )$)�� / � #<) .(#$. 2 . + �,+ ! 2 . �� . � �� / � #<) ! 4(4 # �� . 2'4 #$! � . � � .$#$.�� 5��

�� / � #@) .$#$. 2 . +�� / � #@) � !". + �� / � #@) ( � !". 6 � 7 � . �� / � #<) .(#$. 2 . + �,+ ! 2 . �� . � �� / � #<) ! 4(4 # �� . 2'4 #$! � . � � .$#$.�� 5��:1 � � �

�� / � #@) .$#$. 2 . +�� / � #@) ( � !'. 6 � 7 � . �� / � #<) � !%(�( � . �

�� / � #<) � . 254 #$! � . �� $�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$� � �� / � #@) � . 254 #(! � . 2 ! � � ! � � � � �� / � #@) .$#$. 2 . +�� + ! 2 . � � + � �� / � #@) �"!$#�*'. � (� � .(#$.�� (� ��& � � �

�� / � #<) .$#(. 2 . +�� / � #<) � . 254 #$! � . �� $�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$� � �� / � #@) � . 254 #(! � . 2 ! � � ! � �:1 � �� / � #@) .$#$. 2 . +�� + ! 2 . � �:7 � �

� / � #@) �"!$#�*'. � (� � .(#$.�� (� ��& � � �� / � #<) .$#(. 2 . +��

�� / � #<) � . 254 #$! � . �� $�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$� � �� / � #<) �&�� #(. � !'.$. � �

*=>�+Yb6/2cJ3674KNMGA[<6+Zc2+J7470+Z74-:9;AE14jlMG-4Un9;74KNMGA!1436-H5d9eF6-0MGt^-:9;UgUP+a1036K8LG9;AQ7a�� / 2 # �". 6 �57 ( +(�� & � � . + ��( �87�+ �(� � 1 � � � � � F � � � � �&� ! + � !(#�( + . � � + ( � � �� +�� + �� #( + � 6 . � . &"�� + �� + � � � � � � �GE �� + �� ( 7 � � �

� � � �� D ��

�� + �� #�* � � �� + �� + � � � � � 1�� / �� 1�� + �� ( 7 � � �

� � �� 4 � � �� + � � � � � 1�� 1�� + � �� ##* � � �� + � � � � � � � � �� + �

� _�� 1 -:9;UgUn9;K8-0+21h9;7474-4K8\63E/2+21|+J7)74-:9;AE14jlMG-4Un9;74KNMGAE1 � ��

�� 4 � � �

�� + �

��

<6MGA6AE+J-:9¶u�9;3Rb�K8AE<6+JAi7:9;74KNMGAE1sF6-0´21�z.5N+fF6-0MGt^-:9;UgUP+�9;\E1474-:9;K87|1436K8L^9;Ai7�� / 2 # �". 6 �57 ( +(�� & � � . + ��( �87�+ �(��01 � � � � � F � � � � � �� +�� . � � � + ��

! + ��$6 ! 7�� . & � �)�� . �� . �� . � � + �GE �� + � �� . �� )( 7 � � �� . � � + � D �� + � �� . �

�� . �� 4 #�* � � �� . �� . � � 7�� / �� 7�� . �� )( 7 � � �� . �� . � � 7�� 7�� . �� 4 ##* � � �� . � � + � � �� + � �� . �

�� . �� . �

�� . �

2

I9;-C5?>�+Yb6+JUgF65N+sF6-0/2c2/2<6+JAQ7xoRMGAmLTMGK87HOQ3,> K85�+2147Wj�9GcJK85N+h<6+s74-:9;AE1«jlMG-4UP+J-.36AE+f<6/Y�EA6K874KNMGA�<RK8-4K8tT/2+sFB9;-.5d914ÎqAi7:9±b6+]cx9;5NcJ365d9;Ai7h36A[9;7474-4K8\6367h14ÎQAQ7��E/J74KN10/a+JA¶36AE+Z74-:9;AE1«j�MG-4Un9;74KNMGA � � *=_ %s+JUn9;-0Oi3EMGAE1sc2+JFS+JAE<E9;AQ7OQ3E+|�09;Un9;KN1f<E9;AE1f5N+ecx9;5NcJ365=<D> 36A�9;7474-4K8\6367a9±X?7«X³MGA�\}+210MGK8A�<D>@9Gc2c2/2<6+J-�9;3�c2MGAi70+JAQ3"<6+21Z9;7474-4K8\636701]<6+21A,+f3E<61h�E5N1x_A?.+J7470+eF6-0MGF6-4KN/J70/g<6+�5d9�<6/Y�EA6K874KNMGA~<RK8-4K8tT/2+eFB9;-h5d9�14ÎqAi7:9±b6+e<6+�5?>�+YbR+JUgF65N+e-0+JAE<!F}M^1014K8\65N+1:9�74-:9G<R3EcJ74KNMGA!+JA � � *=_?.MGAE14KN<6/J-0MGAE1.Un9;K8Ai70+JAB9;Ai7C5?>�+Yb6+JUgF65N+|<6+|5d9]14ÎqAi7��E´210+|<D> 36Am10MG36-0c2+s1436-`5d9ft^-:9;UgUn9;K8-0+hF6-0/2c2/2<6+JAQ70+^_�Z9;AE1]5N+mcx9G1a<6+P5d9¶14ÎqAi7��E´210+m<6+P10MG36-0c2+^oIc2MGUgUP+PAEMG3E1�5?>@92LTMGAE1�LQ3 9;3"c��B9;F6K874-0+�F6-0/2c2/2<6+JAi7xo�K85=j?9;3673674K858KN10+J-)36A�1:c��E/JUn9P<6+f74-:9G<R3EcJ74KNMGA�92LT+2c�<6+21|9GcJ74KNMGAE1)K8AQ70/J-4KN+J36-0+21h9;3Rb�-0´Jt^5N+21|<6+fF6-0Mq<R3EcJ74KNMGA,_

�� £Q¥�� w£A�$# ?.MGAE14KN<6/J-0MGAE1apmAEMG36LT+x9;3�5d9�t^-:9;UgUn9;K8-0+gF6-0/2c2/2<6+JAQ70+^_ ?.MGUgUP+eAEMG3E1Z5?>@92LTMGAE1]LQ3~9;3c��B9;F6K874-0+�F6-0/2c2/2<6+JAQ7xo�5N+�10c��E/JUn9!<6+�74-:9G<R3EcJ74KNMGA 1436K8L^9;Ai7�-0/x9;58KN10+�5d9[10ÎQAQ7��E´210+m<D> 36A 10MG36-0c2+�<6+mF6-0M;Xt^-:9;UgUP+apeFB9;-474K8-s<6+Z5?>@9;-4\6-0+]<6+Z<6/J-4K8L^9;74KNMGA��E → E � { 13254 (�� - } T | T

T → T � { 192'4 (�� - } F | F

F → ( { 19254 (��(�� - } E - { 192'4 (�� -3� - } | N { 19254 (�� & �'!(#$#$.0/ - } | I { 192'4 (�� & �'!(#$#$.0/ - }?.+]10c�E/JUn9eF}+J367)10+f74-:9G<R36K8-0+a<6+f5d9eUn9;A6KN´J-0+a1436K8LG9;AQ70+]+JA�� * �

� �� -:9;AE1«jlMG-4Un9;74KNMGAE1h<6+Z<6MqcJ36UP+JAi701 � �!*�� / 2 # �". 6 �57 ( +(�� & � � . + ��( �87�+ �(� � 1 � � � � � F � � � � �&� ! + � !(#�( + . � � � . � � � �� / � #@) �� #$. � !".$. � �". 6 �57 ( +(�� & � � / 2 # + � ) / � # � � ! � �$4 ) �� & � D & ( 6 � � �&�� +$6 ! + � )( 602 � �� / � #@) (#* �$4 * � 2 . � !�( �$�� .0/ � � 7�+)� . +��(� � + ( � . + �#( �87�+ �$��01 � � � � � F � � � � � �� / � #@) ��(687�4 ��4 !��0. .$#$. 2 . +�� :��:� � � �� $�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(� � �� / � #@) � . 254 #(! � . 2 ! � � ! � � � � �� / � #@) � !�( ( � . �� / � #@) �)!'. + � . �&�(�� ! 7 # � )$) � ##* � � �� / � #<) ! 4$4 # �� . 2'4 #(! � . � � .$#(.�� 5�� / � #<) � .:/ � �0� �� / � #<) � .0/ � �� / � #<) ! 4$4 # �� . 2'4 #(! � . � � .$#(.�� 5�� + � � �

�� / � #@) � !". + �� / � #@) ( � !". 6 � 7 � . �� / � #<) ! 4$4 # �� . 2'4 #(! � . � � �

�� / � #@) ( � !'. 6 � 7 � . �� / � #<) � !%(�( � . �

�� / � #<) � . 254 #$! � . �� $�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(� � �� / � #@) � . 254 #(! � . 2 ! � � ! � � + � �� / � #@) � !�( ( � . �� / � #@) �)!'. + � . �&�(�� ! 7 # � )$) � ( 7 � � �

� / � #<) ! 4$4 # �� . 2'4 #(! � . � � .$#(.�� 5�� + � � �� / � #<) � .:/ � �5� �� / � #<) � .0/ � �� / � #<) ! 4$4 # �� . 2'4 #(! � . � � .$#(.�� 5��

�� / � #@) � !". + �� / � #@) ( � !". 6 � 7 � . �� / � #<) ! 4$4 # �� . 2'4 #(! � . � � �

�� / � #@) ( � !'. 6 � 7 � . �� / � #<) � !%(�( � . �

�� / � #<) � . 254 #$! � . �� $�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(� � �� / � #@) � . 254 #(! � . 2 ! � � ! � � � � �� / � #@) � !�( ( � . �� / � #@) �)!'. + � . �&�(�� ! 7 # � )$) � � �� / � #<) � .:/ � � ( �� / � #<) � .0/ � �� / � #<) ! 4$4 # �� . 2'4 #(! � . � � .$#(.�� 5�� / � #<) � .:/ � � - �� / � #<) � .0/ � �

�� / � #@) � !". + �� / � #@) �)!'. + � . �&�(�� ! 7 # � )$)�� / � #<) �"!$##*". � (� � .$#(.�� (��

�� / � #@) � !". + �� / � #@) ( � !". 6 � 7 � . �� / � #<) �"!$##*". � (� � .$#(.�� (��01 � � �� / � #@) ( � !'. 6 � 7 � . �

�� / � #<) � !%(�( � . �� / � #<) � . 254 #$! � . �� $�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(� � �� / � #<) �&�� #(. � !'.$. � �

2

� _ � � =Í.� � � +J7H5d9e74-:9;AE1«j�MG-4Un9;74KNMGA[<6+Z<6MqcJ36UP+JAi701 � � �

� ¸�� º�� ÆIÀ&Ê0É ÀBÄ}É)¾�Á��HÄ�� ÉCÀ�¿��|¾ Â�Æ Â � �� Æ�¾sÀ�Á� K�5N+a5d9;A6ti9;tT+�<6+�74-:9;AE1«j�MG-4Un9;74KNMGA � � *�K8UgFSM^10+�<6+21hc2MGAi74-:9;K8Ai70+21f70+J585N+21fOQ3,> K85�+2147hK8UgF}M^1014K8\65N+a<D> Îcx9;5NcJ365N+J-W+>=D+2cJ74K8LT+JUP+JAi7.<6+21W9;7474-4K8\636701.9;3n10+JAE1=<6+21�t^-:9;UgUn9;K8-0+21C9;7474-4K8\63E/21xoi5?> � =ÍI�� <6MGA6AE+)c2+J7470+

� +YbRK8\6K858K870/^_�� +2147]36AE+nK8Ai70+J-«j?9Gc2+m147:9;AE<E9;-0<RKN1:/2+mOQ36K=F}+J-4UP+J7�<6+P-0/2cJ36F}/J-0+J-a5?>@9;-4\}MG-0+210c2+JAEc2+�<D> 36A<6MqcJ36UP+JAi7�� [* 1:MG3E1�5d9�jlMG-4UP+�<D>�MG\R�4+J701�Un9;A6K8F6365d9;\65N+21[<E9;AE1�36AÈ5d9;A6ti9;tT+"<6+[F6-0MGt^-:9;UgUn9;74KNMGA,_�583E14KN+J36-01hK8UgF65d9;AQ7:9;74KNMGAE1Z<6+ac2+J7470+ � =ÍH+YbRKN1470+JAi7f<E9;AE1s5N+21)5d9;A6ti9;tT+21ZpPMG\R�4+J701sc2MG36-:9;AQ701xoS<6MGAi7 �i92L^9+J7 �Îq7��EMGA,_B*�9g58K8\6-:9;K8-4KN+ �h+J-0c2+21yoRFB9;-|+YbR+JUgF65N+ôB+JA¶<6MGA6AE+Z36AE+ZK8UgF65d9;AQ7:9;74KNMGA[F}MG36-��i92L^9R_� �� &� ��

2�3E+s<6+|Un9;A6KN´J-0+s74-0´21WtT/JAE/J-:9;5N+ôq5?> � `Í�� 70+J585N+hOQ3E+|<6/Y�EA6KN+sFB9;-W5N+�� G? c2MGAE14KN1470+s+JA�<RKkbqX³10+JF67K8Ai70+J-«j?9Gc2+21h+J7H36AE+a+Yb6c2+JF674KNMGA�uw5d9��Et^36-0+ � _��Z+JA¶F6-0/210+JAi70+JAQ7s5N+21|F6-4K8AEcJK8FB9;5N+21�zHOQ36K,c2MGUgUn9;AE<6+JAi7fc2MGUeXUP+JAi7f9Gc2c2/2<6+J-s9;3Rb�<RK =}/J-0+JAQ701|7ÏÎQF}+21)<6+fA,+f3E<61|<E9;AE1|36A¶9;-4\6-0+]<6+]<6MqcJ36UP+JAi7 � �!*=_6*,+21|K8Ai70+J-«j?9Gc2+21��( � .m+J7 � #$. 2 . +�� <6/Y�EA6KN1010+JAQ7f5N+21|UP/J7��EMq<6+21hFS+J-4UP+J747:9;AQ7]<6+aAB9xLQK8t^3E+J-Z<E9;AE1s5?>@9;-4\SMG-0+210c2+JAEc2+ô}K8AQ70+J-«X-0MGtT+J-.36AnA,+f3E<mFSMG36-C+JAmc2MGA6AB9��N74-0+h5N+)7ÏÎQF}+hMG3m+JAEc2MG-0+s5N+|AEMGU <D>�/J5N/JUP+JAi7xoRMG3�+JAEc2MG-0+|F}MG36-ÙPMq<RKk�B+J-5?>@9;-4\6-0+ôE+JA[9±�4MG367:9;Ai7s36A¶9;7474-4K8\6367h9xLT+2c]1:9�L^9;5N+J36-sp�36A¶/J5N/JUP+JAi7sFB9;-)+YbR+JUgF65N+^_�MG36-W74-:9;AE1«jlMG-4UP+J-W36An<6MqcJ36UP+JAi7 � �!*=o^K85B103*)P7`<6MGAEc|<6+H58K8-0+|c2+)<6MQcJ36UP+JAQ7.+JAn3674K858KN1:9;Ai7W36Am9;AB9±X58ÎR10+J36-)Oi36KD-0+J70MG36-4AE+]36A[9;-4\6-0+Z<6+]<6MqcJ36UP+JAi7)-0+214F}+2cJ7:9;Ai7s5?> � `ÍW�� oRF636KN1)<6+f74-:92LT+J-010+J-hc2+J7|9;-4\6-0+F}MG36-H5836K�9;F6F658KNOi3E+J-|5N+21HUPMQ<RKk�Bcx9;74KNMGAE1f9;7470+JAE<R3E+21xoE+J7)�EAB9;5N+JUP+JAi7|-0/2/2cJ-4K8-0+]5?>@9;-4\6-0+ac2MGUgUP+Z36A¶<6MqcJ3RXUP+JAi7 � �[*�<E9;AE1|36A��Bc�6KN+J-s-0/21036587:9;7x_B*�9n<RKN1474-4K8\63674KNMGA!<6+ �h+J-0c2+21sc2MGAi74KN+JAQ7h36AE+�cJ5d9G1010+ � � � � 687�� . 6OQ36KEK858583E1474-0+)c2MGUgUP+JAQ7.9;AB9;58ÎR10+J-=36An<6MqcJ36UP+JAi7WFSMG36-`+JAn-0/2cJ36FS/J-0+J-W36An9;-4\6-0+ôTF636KN1`c2MGUgUP+JAQ7.9 )nc�E+J-c2+J7=9;-4\6-0+Cc2MGUgUP+W36Ae<6MqcJ36UP+JAi7 � �[*�9;3�70+J-4UgK8AB9;5?_^¬|AE+.14K8UgF65N+.-0+2<RK8-0+2cJ74KNMGAP143*)P7IFSMG36-�+JA�-0+JLT+J-010+J-5N+gc2MGAi70+JAQ3�<E9;AE1Z36A��Bc�6KN+J-x_,ÍÏ5�103*)P7]<6MGAEcP<6+�UPMQ<RKk�B+J-]5N/JtT´J-0+JUP+JAQ7�c2+J7470+gcJ5d9G101:+eFSMG36-ZK8AQ70+J-4LT+J-474K8-36AE+Z74-:9;AE1«j�MG-4Un9;74KNMGA�3674K858KN1:9;AQ7s�� +JAi74-0+]5?>@9;AB9;58ÎR10+]<R3��Bc�6KN+J-s10MG36-0c2+a+J7H5?>�/2cJ-4K87436-0+a<R3�-0/21436587:9;7x_�MG36-�K858583E1474-0+J-�5?> 3674K858KN1:9;74KNMGAÈ<6+[5?> � =Ín� � ��o.c2MGAE14KN<6/J-0MGAE1�5N+¶F6-0MG\65N´JUP+�<6+[-0/2cJ36FS/J-0+J-�36A 7:9±X\65N+x9;3�<6+21f/J5N/JUP+JAi701]<D> 36A�c2+J-47:9;K8A�AEMGU FB9;-4UgK�5N+21sA,+f3E<61s�E5N1Z<D> 36A�c2+J-47:9;K8A�/J5N/JUP+JAi7x_D*�9mUP/J7��EMq<6+

�. � � ! 7 # �G6 . + � #$. 2 . + � �� '! 2 .P1436K8LG9;AQ70+Z-0/x9;58KN10+Zc2+J7470+Z-0/2cJ36F}/J-:9;74KNMGA��

4$6 ( � .�� . � � #$. 2 . +�� . � � ! 7 # �$6 . + � #(. 2 . +�� '! 2 . �� #$. 2 . + � .$#(. 2 . +�� '5!:�'! & #(! + �-& � �$687 + � + ! 2 .

-!

�%( � . ! � ! 7 # � ��( � . �

�%( � . 7 �� ! 7 # �G6 . + �

� #$. 2 . + � � � 6 . � ��G254 �

7 +�� .(#$. 2 . + � � (#* + � ��7 �

��! 7 # �G6 . +�� .$#$. 2 . +��-& � . � � ! 7 # � ��( � . � � - �7 +�� + (�� ! 7 # �G6 . + � � ! 7 # �$6 . + & � . � . + � � !"� - ��G254��,+ .�� #$. 2 . + � � + (�� ! 7 # �G6 . + � �

.(#$. 2 . + � � (�* + � � � �

�( 6 � 7 � � � 7 � + (�� ! 7 # �G6 . + � 7 �(� - !! � ! 7 # � �%( � . � � ! 7 # �$6 . +-&�7�� . 2 � 7 - �7 #�! � ! 7 # � ��( � . & � . � ��( � . +��$4 . � - �(� �%( � . & � �� +%$ � �� '&(&

�(� � #$. 2 . +�� - ! � ! 7 # � �%( � . - & � . � + ! � �'! 2 .)� - & . � *'!$# � � + ! 2 . - - !�G254 � .$#(. 2 . +�� (�* +��5�$� � � � � #$. 2 . + � - ! � ! 7 # � ��( � . �

� �0� -:9;AE1«jlMG-4Un9;74KNMGAE1h<6+Z<6MqcJ36UP+JAi701 � �!*

� �S¦x£Q°��Ï��T£i¢� ��(6 -0+JF6-0/210+JAQ70+Z36A[9;7474-4K8\6367h<E9;AE1H36A¶MG\R�4+J7 � #$. 2 . +�� _� !'! 6 !�� . 6 �'! � ! /J70+JAE<�5?> K8Ai70+J-«j?9Gc2+ ��( � .�92LT+2cm36A�+JAE1:+JUa\65N+�<6+nUP/J7��EMq<6+21�FSMG36-9Gc2c2/2<6+J-spe<6+21|<6MGA6AE/2+21|<6+Z7ÏÎQF}+Zcx9;-:9GcJ70´J-0+^_� ( 2(2 . + � �E/J-4K870+h<6+ � !'! 6 !�� . 6 �'! � !�+J7.-0+JF6-0/210+JAi70+h5N+hc2MGAi70+JAQ3�<D> 36A�c2MGUeXUP+JAQ7:9;K8-0+^_�%(��* 2 . +�� -0+JF6-0/210+JAQ70+Z36A¶<6MqcJ36UP+JAi7 � �!*~+JAi74KN+J-x_�%(��* 2 . +�� +��$4 . -0+JF6-0/210+JAQ70+~5N+�7ÏÎQF}+~<6+~<6MqcJ36UP+JAi701�+J7�5N+21�K8ARjlMG-4Un9;74KNMGAE1!Oi3,> K85c2MGAQ74KN+JAi7�uwAEMGU�<6+Z5d9e� ��oB+JAi74K870/21xo,_8_8_ zY_� � � 19254 #$. 2 . + � ! �87 ( + F6-0MGF}M^10+h<6+21`UP/J7��EMq<6+21CFSMG36-.MG\670+JA6K8-H<6+|5?> K8ARj�MG-4Un9;74KNMGA�<6+|5?> K8UeXF65d9;AQ7:9;74KNMGAµ10MG3E1«X8�09Gc2+JAi70+[<6+�� <6+�Un9;A6KN´J-0+�K8AE<6/JF}+JAE<E9;Ai70+<6+f5?> K8UgF65d9;AQ7:9;74KNMGA,_� #$. 2 . + � �E/J-4K870+]<6+ �%( � .g+J7)-0/JF6-0/210+JAQ70+]36A�/J5N/JUP+JAQ7s<E9;AE1)5N+Z<6MqcJ36UP+JAi7x_�%( � . -0+JF6-0/210+JAQ70+|5N+)7³ÎqFS+s<6+|<6MGA6AE/2+21W5N+)F6583E1=tT/JAE/J-:9;5}<6+)5?> � =Í�� o36A�A,+f3E<�<E9;AE1|5?>@9;-4\6-0+]<R3�<6MqcJ36UP+JAi7x_�%( � . 7 �� -0+JF6-0/210+JAQ70+h36AE+s9;\E1474-:9GcJ74KNMGA�1436-W36AE+sc2MG585N+2cJ74KNMGA�<6+sA,+f3E<61W<E9;AE136A�<6MqcJ36UP+JAi7x_+ .:/ � �E/J-4K870+�<6+ � !'! 6 !�� . 6 �'! � ! +J7¶-0+JF6-0/210+JAi70+�5N+"c2MGAi70+JAi3%70+Ybq743E+J5<D> 36A�/J5N/JUP+JAQ7sMG3¶<D> 36A[9;7474-4K8\6367x_ �� T£(��¦y§"!��¢� � � � / �0. 4 �87 ( + +Yb6c2+JF674KNMGA�5N+JLT/2+Z5NMG-010OQ3,> 36AE+]MGF}/J-:9;74KNMGA¶+2147HK8UgF}M^1014K8\65N+^_

�� _�� ÍÏAi70+J-«j?9Gc2+21|<6+f5?> � =Í.� � ��<R3 � �G?h_

�� . +)� (� 7 #� - �� . + � (� )( 6 � -

6 . ��,+ .�� #$. 2 . + � � .(#$. 2 . + � � (#* + � � �

�( 6 � 7 � � � 7 � .$#(. 2 . +�� (#* +�� 7 �(� - !6 . � � 7 � � �G254 � 7 � �

�� . + � (� )( 6 � -

6 . � * 6$+ 6 . � �

�� . � � ! 7 # �G6 . + � #$. 2 . + � (� ��'! 2 .)� -

*=> K8Ai70+J-«j?9Gc2+ � #$. 2 . + � AEMG3E1WM�=S-0+H5d9ZUP/J7��EMQ<6+ � . � + ! � �'! 2 .]FSMG36-�-0/2cJ36F}/J-0+J-`5N+)AEMGU <D> 36An/J5N/JUP+JAQ79;5NMG-01)OQ3E+Z5?> K8Ai70+J-«j?9Gc2+��%( � .eAEMG3E1)M�=}-0+Z5N+21HUP/J7��EMq<6+21]��

. � � ! 7 # � ��( � . � OQ36KD-0+J70MG36-4AE+Z36AE+Z58KN1470+nu �%( � . 7 �� z.<6+21HA,+f3E<61H�E5N1)<R3�-0+2c2+JLT+J36-xo�+J7� �

. � ��( � . +��$4 . � - OQ36K,-0+J70MG36-4AE+]5N+a7³ÎqFS+a<6+ZA,+f3E<¶10MG3E1|5d9ej�MG-4UP+]<D> 36A[+JAQ74KN+J-hc2MG36-47eu � !%( 6�� zHpc2MGUgFB9;-0+J-s9;3Rb�c2MGAE147:9;Ai70+21|F6-0/2<6/Y�EA6KN+21s<E9;AE1)5?> K8Ai70+J-«j?9Gc2+��( � . �� LT+2cHc2+21�UP/J7��EMq<6+21xoGK85E+2147Ij?9GcJK85N+H<6+C-0/2cJ36FS/J-0+J-�5N+21��E5N1yo;<D> K870/J-0+J-W1436-�c2+J3RbQX³cJKE<6+CUn9;A6KN´J-0+|ps-0+JF}/J-0+J-5N+21ZA,+f3E<61�/J5N/JUP+JAi701�<R3~AEMGU <6MGA6AE/n+J7�<6+e5N+21�9Gc2cJ36Ua365N+J-�<E9;AE1]36A~7:9;\65N+x9;3 uwFB9;-]5?> K8Ai70+J-4UP/2<RKd9;K8-0+<D> 36A�7:9;\65N+x9;3�70+JUgFSMG-:9;K8-0+e<6+�Un9;A6KN´J-0+PpncJ-0/2+J-f36A!7:9;\65N+x9;3�<6MGAQ7f5d9P7:9;K8585N+ec2MG-4-0+214F}MGAE<�+Yb69GcJ70+JUP+JAQ79;3�AEMGU�\6-0+]<D>�/J5N/JUP+JAi701s-0+J70MG36-4AE/21�zY_¬|AE+H7�Gc�E+s9fF6-4KNMG-4K�36APF}+J3PF6583E1`14K8UgF65N+sc2MGAE14KN1470+|pZLT/J-4Kk�B+J-W1x> K85B+YbRKN1470+CFB9;-4UgK�5N+21=A,+f3E<61��E5N1W<D> 36A/J5N/JUP+JAi7a36A~Oi36K=10MGK87f36A~/J5N/JUP+JAQ7a<D> 36A"c2+J-47:9;K8A�AEMGU�_A;�A�3674K858KN1�9;Ai7]5N+�UPVJUP+P10c�E/JUn9�Oi3E+eF}MG36-Z5d9

� _ � � =Í.� � � +J7H5d9e74-:9;AE1«j�MG-4Un9;74KNMGA[<6+Z<6MqcJ36UP+JAi701 � ��

UP/J7��EMq<6+nF6-0/2c2/2<6+JAQ70+ô�5d9�UP/J7��EMq<6+�!"! � � ! 7 # � � #$. 2 . +�� "! 2 .[1436K8L^9;Ai70+�-0/x9;58KN10+�c2+J7470+mLT/J-4Kk�Bcx9;74KNMGA+JA"MGF674K8UgKN1:9;AQ7�5?> K870/J-:9;74KNMGA 1436-]5N+21aA,+f3E<61]�E5N1�<6+gUn9;A6KN´J-0+mp�70+J-4UgK8AE+J-�<6´21�Oi3,> 36A�/J5N/JUP+JAi7��E5N1a<R3\}MGA�AEMGU +2147H74-0MG36LT/n�

4$6 ( � .�� . �� (�((#$.(! + !'! � � ! 7 # � � #(. 2 . +�� "! 2 . �� #$. 2 . + � .$#(. 2 . +�� '5!:�'! & #(! + �-& � �$687 + � + ! 2 .-

!

�%( � . ! � ! 7 # � ��( � . �

�%( � . 7 �� ! 7 # �$6 . +,� .$#(. 2 . +�� & � . � � ! 7 # � �%( � . � � - �7 +�� + (�� ! 7 # �G6 . + � � ! 7 # �$6 . + & � . � . + � � !"� - ��(�($#(.$! + !"! � � ! 7 # � � #$. 2 . +�� '!$# � . �

�( 6 � 7 +�� 7 � � � �$!"! � � ! 7 # � � #$. 2 . + � &(& 7 � + (�� ! 7 # �G6 . + � 7��$� - !! � ! 7 # � �%( � . � � ! 7 # �$6 . +-&�7�� . 2 � 7 - �7 #�! � ! 7 # � ��( � . & � . � ��( � . +��$4 . � - �(� �%( � . & � �� +%$ � �� '&(&

�(� � #$. 2 . +�� - ! � ! 7 # � �%( � . - & � . � + ! � �'! 2 .)� - & . � *'!$# � � + ! 2 . - - !!"! � � ! 7 # � � #$. 2 . +�� (6 *". �

�� . +)� (� 7 #� - �� . + � (� )( 6 � -

6 . � * 6$+ !'! � � ! 7 # � � #$. 2 . + � �

�� !'! � � ! 7 # � � #(. 2 . +�� (� ��"! 2 . � -

� �� *��$!"� �� %�$ �&� ��

*=>�MG\R�«+2cJ74KkjZOQ3E+mAEMG3E1PAEMG3E1��6bRMGAE1g+2147g<D>�/JL^9;583E+J-g5N+21n9;7474-4K8\636701P<D> 36AE+�t^-:9;UgUn9;K8-0+�*DXÏ9;7474-4K8\63E/2+ô+JA[1036F6FSM^1:9;AQ7sOQ3E+]5d9Pt^-:9;UgUn9;K8-0+e9P/J70/]UPMq<RKk�B/2+aF}MG36-|-0+JUgF65d9Gc2+J-h5N+21h9Gc2c2´21f9;3Rb[9;7474-4K8\636701��E/J-4K870/21FB9;-)<6+21|9Gc2c2´21)<E9;AE1)5d9�F6K85N+ôEc2MGUgUP+ZAEMG3E1H5?>@9xLTMGAE1)Lq3¶pa5d9e�EA�<6+f5d9e10+2cJ74KNMGA�F6-0/2c2/2<6+JAi70+^_�?.+J7)MG-0<R-0+<D>�/JL^9;583B9;74KNMGA"c2MG-4-0+214F}MGAE<"p�36A�FB9;-0c2MG36-01a<6+e5?>@9;-4\6-0+P<6+eti9;3Ec�E+mp�<R-0MGK870+P+JA�F6-0M;j�MGAE<6+J36-a<D>@9;\}MG-0<D_IMG36-a5N+21]\}+210MGK8AE1�<6+g5?>�/JLG9;583B9;74KNMGA <6+21�9;7474-4K8\636701yo,K85�j?9;367aVJ74-0+ncx9;FB9;\65N+m<6+nc2MGAE10+J-4LT+J-�5N+21a/J5N/JUP+JAQ701<6/ �0pZ74-:9;K870/21C<E9;AE1`36AE+|F6K85N+sMG{mK85�+2147WFSM^1:14K8\65N+)<D>@9Gc2c2/2<6+J-)9;3Rbn/J5N/JUP+JAi701.-0+J5d9;74K8LT+JUP+JAi7|p]5?>�/J5N/JUP+JAi7H+JA10MGUgUP+J7I<6+=F6K85N+^_x*�9H�Et^36-0+ � _��)F6-0MGFSM^10+`36AE+=cJ5d9G1010+W<6/J-4K8LT/2+`<6+`5d9HcJ5d9G1010+=107:9;AE<E9;-0<�'(!0�'! & * � 7 # & � � !��<6+Z5d9�58K8\6-:9;K8-4KN+ �i92L^9eF}MG36-)c2+fj�9;K8-0+^_*=>@9;58tTMG-4K87��6UP+Z<6+)FB9;-0c2MG36-01C<6+JLqKN+JAi7H9;5NMG-01W-0+J5d9;74K8LT+JUP+JAQ7H14K8UgF65N+^_(;=AmFB9;-47:9;AQ7C<6+|5d9Z-:9GcJK8AE+ôqK85Ej?9;36774-:9;K870+J-�5N+21�A,+f3E<61I�E5N1=<6+.ti9;3Ec�E+|pf<R-0MGK870+)92L^9;Ai7`<6+.74-:9;K870+J-=5N+.A,+f3E<gFB9;-0+JAQ7x_T*,MG-01�<R3g74-:9;K870+JUP+JAQ7W<R3A,+f3E<gFB9;-0+JAQ7xoT5N+21�A,+f3E<61=�E5N1=10MGAi7W<6/JF6K85N/21xo^F636KN1=MGAn<6MGK87`74-:9;K870+J-=5N+CA,+f3E<PFB9;-0+JAQ7W92L^9;Ai7.<6+C5?>�+JUgF6K85N+J-pe10MGA�70MG36-)<E9;AE1|5d9�F6K85N+]<6+ZA,+f3E<61H74-:9;K870/21y_�58367��G7.OQ3E+)<6+s<6MGA6AE+J-`36A�9;58tTMG-4K87��6UP+stT/JAE/J-:9;5?oqc2MGAE14KN<6/J-0MGAE1`5d9ac2MGAE1474-43EcJ74KNMGA�<D> 36AE+)74-:9;AE1«j�MG-4Un9±X74KNMGA�FB9;-|<6+21:c2+JAi70+Z-0/2cJ36-014K8LT+]K858583E1474-0/2+ZFB9;-)36A¶+Yb6+JUgF65N+ZF6-0/2cJKN1x_

�� £Q¥�� w£A�� ?.MGAE14KN<6/J-0MGAE1sp�AEMG36LT+x9;3[5d9�t^-:9;UgUn9;K8-0+�9;\E1474-:9;K870+�<6+f5d9g10+2cJ74KNMGA�F6-0/2c2/2<6+JAQ70+m�

e → e � e | e � e | n | i

�� -:9;AE1«jlMG-4Un9;74KNMGAE1h<6+Z<6MqcJ36UP+JAi701 � �!*

� �(�� ( � . � � � !�� 7 � !��'.(#$! � 7 �".�� :. � � �� ( � . � .0/ � . + � � � !'. �&� ! +)� ! 6 �� ( � . � '5!:�'! & * �87 # & � � !�� #( � . � �0#$! � � 7�+ ( 6)� . 6 � ( 4(6 (0� 7�� . ! +� !��:. � � � ( �� !�� .(#$. 2 . + � � �� ! + 7�+)� .0/ 6 .$#(! �87 �'. � ( � !'. � ( 4� .$#(. 2 . +�� 7�+ � !'. �� !�� &�� 4 � � 6 .$! � . � ) + !�* � ! � �� ) � � ) D)� �� D �� 4 �� !�* � !%( 6 �

!��*'. � � !$#$. + '! +��

� � �". 6 �57 ( + � & � � � � F � �� D� �4 * � # 7 � �0#$! � � � � !�� 7 � !��'.(#$! � 7 �".�� :. � � .:/ � . +)� � '(!0�'! & * � 7 # & � � !�� !

� �$�� .$. � � �!��:. � � . � � 7�� !�(�* � 6 . 2 (0� 7�+ � - ! �� !�� .$#(. 2 . +�� ! �� #( � . �"7�+)� .:/ �� #( � . � 4 ( �(7��87 ( + � * +)� . 6 � !'. � ( 4 (� � !'. �&� !�� ( � . �'7 + � .0/ �� #( � . � �(� � 2 .$! + � � !'. � ( 4 (� � !". �� !�� - &�� 4 ! 6 ! 2 7 + � .0/ � !'. 4 ( �(7 � 7 ( + 6 ( 2 � !'. � ( 4 � ( !��0. � � &� � 6 . � * 6(+ � !'. !��:. � � . � .(#$. 2 . + � � ��7 7�� .:/ 7 �� &� � .:/ �:. 4 �87 ( + '(!0�'! & * � 7 # & � 2'4�� !�� / �:. 4 �87 ( + � !'. + � !'. 6 . 7 � + (� � * � ! .(#$. 2 . + � 7 + � !'. �� !�� &� �4 * � # 7 � �

�'(.�� 4 .$. �� 7 +�� 7�+ � .:/ -

� ! 6 (�� '(!:�"! & * �87 # & � 254 �� !�� / �0. 4 �87 ( +!

��'(.�� 6 . � �

7 #�.(#$. 2 . + � � (#* + � �0� 7�+)� .:/ - !6 . �� .$#(. 2 . +�� '! � ! � .$#$. 2 . +�� (#* +�� 7 + � .0/ � � - � �

.$# � . !

� ! 6 (�� + .�� '5!:�"! & * �87 # & � 254 �� !�� / �0. 4�� 7 ( + � - � �� . +)� (� 7 #� - .$# � .6 . � * 6(+ 6 . � �

�� 4 .$. �� - �� $�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$�(�$�$�(�$� �:#(! � � � � !�� 7 � !��'.(#$! � 7 �".�� :. � �

�� _�� *�9gcJ5d9G1:10+ � � !�� 7�� !��".$#(! �87 �'.�� 0. � �+J7H5d9g� ��c2MG-4-0+214F}MGAE<E9;Ai70+ ! � �&�$6 ! 7 � . & � � � �� / 2 # �". 6 �57 ( +(�� & � � . + ��( �87�+ �(� � 1 � � � � � F � � � � � �� + .��(�. � 4 ##* � � . -�� . � �( 7 � � . -�� + � 7 - �� + + � � � � �� + � - �� + 7 � � � � �� + � - �� + 4 #�* � �� +��

� _ � � =Í.� � � +J7H5d9e74-:9;AE1«j�MG-4Un9;74KNMGA[<6+Z<6MqcJ36UP+JAi701 ��

� � � �� + )( 7 � �� +��

¬|AE+eMGF674K8UgKN1:9;74KNMGA"OQ3E+�jlMGAQ7f70MG3E1f5N+21Zc2MGUgF6K85d9;70+J36-01]<RK8tÂE+21]<6+ec2+�AEMGU c2MGAE14KN1470+gp�/JLG9;583E+J-apm5d9c2MGUgF6K85d9;74KNMGA,oic^>�+2107«XÏp±X³<RK8-0+)147:9;74KNOQ3E+JUP+JAi7xo^5N+21=+YbRF6-0+21014KNMGAE1`c2MGAE147:9;Ai70+21x_i�f9;AE1=5N+.cx9G1`<6+C5d9ht^-:9;UgUn9;K8-0+9;\E1474-:9;K870+nF6-0/2c2/2<6+JAi70+ôI70MG3670+m+YbRF6-0+21014KNMGA"AE+nc2MGUgF}MG-47:9;Ai7eOi3E+m<6+21]AEMGUa\6-0+21�F}+J367�VJ74-0+mc2MGAE14KN<6/J-0/2+c2MGUgUP+fc2MGAE147:9;Ai70+^_"�9;-Hc2MGAi74-0+ôq36AE+f+YbqF6-0+21:14KNMGA�OQ36K}c2MGAi74KN+JAi7)<6+21.KN<6+JAQ74Kk�Bcx9;70+J36-01)<6MGK87HVJ74-0+s/JL^9;583E/2+p¶5?>�+YbR/2cJ3674KNMGA,o�c^>�+2147«XÏp±X³<RK8-0+�<RÎqAB9;UgKNOi3E+JUP+JAQ7xo�F636KN10OQ3,>�MGA�AE+�c2MGA6AB9��N7eFB9G1e147:9;74KNOi3E+JUP+JAQ7e5d9�L^9;5N+J36-<6+21HL^9;-4Kd9;\65N+21x_*=>@9;AB9;58Îq1:+aOQ36K�c��E+J-0c�E+�pe-0/JFB9;-474K8-h5N+21)+YbRF6-0+21014KNMGAE1s+JAi74-0+�c2+J585N+21|OQ36K�10MGAi7h/JLG9;583B9;\65N+21s147:9;74KNOQ3E+a+J7c2+J585N+21fOi36KI5N+�10MGAi7Z<RÎqAB9;UgKNOi3E+JUP+JAQ7]+2147h9;F6F}+J5N/2+g9;AB9;58Îq10+�<6+21hUPMGUP+JAi701Z<6+�58Kd9;KN10MGA u 76¯Y�w� � �w�QGÐÏ�l�w�n��G��^��;��v� 96zY_yÍ cJK?oy+J585N+W+2147�74-0´21I14K8UgF65N+ô±F636KN10Oi3E+`FB9;-�<6/Y�EA6K874KNMGAe36AE+`+YbRF6-0+21014KNMGA�c2MGAi70+JAB9;AQ7�36A6KNOi3E+JUP+JAQ736A�AEMGUa\6-0+g+2107f107:9;74KNOi3E+ôD+J7Z70MG3670+g+YbRF6-0+21014KNMGA�<D>@9G<6<RK874KNMGA"MG3�<6+eUa365874K8F658KNcx9;74KNMGA�Oi36K�1x>@9;F6F658KNOQ3E+Pp<6+J3Rba10MG3E1«X³+YbRF6-0+21014KNMGAE1�147:9;74KNOQ3E+21�+2147I+J585N+YX?UPVJUP+W107:9;74KNOi3E+^_±�f9;AE1�70MG3E1�5N+21�9;3674-0+21�cx9G1xo25N+21I+YbqF6-0+21:14KNMGAE110MGAQ7f<RÎqAB9;UgKNOQ3E+21x_D*�9�<6/Y�EA6K874KNMGA"<RK8-4K8tT/2+eFB9;-f5d9�14ÎQAQ7:9±bR+e1436K8L^9;Ai70+e-0+JAE<�c2MGUgF670+g<6+gc2+J7470+�KN<6/2+g+JA+YbRF6-4K8Un9;Ai7|5N+Zcx9;5NcJ365�<D> 36A[9;7474-4K8\6367 2 #�uwF}MG36-)UPMGUP+JAi7h<6+f58Kd9;KN10MGA�zf��-0MQ<R3EcJ74KNMGAE1 %|´Jt^5N+21e→ e1 � e2 �(7 e1 & 2 # �$� �Y�?�T� &(&

e2 & 2 # �$� �J�?�^� !$# ( 6 � e & 2 # � �Y�?�^��(7 + ( + e & 2 # � � �G�

e→ e1 � e2 �(7 e1 & 2 # �$� �Y�?�T� &(&e2 & 2 # �$� �J�?�^� !$# ( 6 � e & 2 # � �Y�?�^�

�(7 + ( + e & 2 # � � �G�e→ n e & 2 # � �J�?�^�e→ i e & 2 # � � �G�*=> KN<6/2+]<6+f5d9�F6-0MGt^-:9;UgUn9;74KNMGA[<6+f5d9�74-:9;AE14jlMG-4Un9;74KNMGA!+2147C5d9e1436K8LG9;AQ70+^_E�e>@9;\SMG-0<Do6MGA�1036F6FSM^10+ZOQ3E+5d9�74-:9;AE1«j�MG-4Un9;74KNMGA[+2147H5d9;AEc2/2+aFB9;-H5d9eUP/J7��EMq<6+]1436K8L^9;Ai70+P�4 * � # 7 � �%( 7&� �$6 ! + � )( 6G2 ��%(�� * 2 . +�� (�� * 2 . + �

-!

� ! 7 � &$�(6 ! + � �( 602 � #(. 2 . +�� (�� * 2 . + �-& � . � ��(�� * 2 . + � � #(. 2 . +�� - - � �� (6 ! + � �( 6G2 � -

OQ36KE-0/2cJ36FS´J-0+|5?>�/J5N/JUP+JAi7.-:9GcJK8AE+|<R3�<6MQcJ36UP+JAQ7`-0+2rJ3m+JAmFB9;-:9;UP´J74-0+^_Q*`> KN<6/2+|+2147`<D>�/2cJ-4K8-0+|36AE+)UP/J7��EMq<6+<6+s74-:9;AE1«jlMG-4Un9;74KNMGA�F}MG36-Cc��B9GOQ3E+s7ÏÎQF}+h<D>�/J5N/JUP+JAi701H<E9;AE1.5N+f<6MQcJ36UP+JAQ7x_"�sA�<6MGK87H<D>@9;\SMG-0<�/2cJ-4K8-0+s36AE+UP/J7��EMq<6+]<D>@9;K8t^36K8585d9;tT+aOQ36K?oE/J7:9;Ai7s<6MGA6AE/Z5N+ZAEMGU <6+f5?>�/J5N/JUP+JAQ7xo�9;F6F658KNOQ3E+]5d9�\}MGA6AE+ZUP/J7��EMQ<6+n�4$6 ( � .�� . � ��( 7&� �$6 ! + � )( 6G2 � #$. 2 . + � �� #$. 2 . + � .(#$. 2 . + �

-!

7 � .$#$. 2 . +��-& � . ��+ ! � �"! 2 .)� - & . � *'!(# � � � . � -�- !� ! 7 � &"�$6 ! + � )( 602 $ . � .$#$. 2 . +�� - � .$# � . 7 #� .$#$. 2 . +��-& � . ��+ ! � �"! 2 .)� - & . � *'!(# � � � + � -�- !� ! 7 � &"�$6 ! + � )( 602 $0+ � .$#$. 2 . +�� - �

�� -:9;AE1«jlMG-4Un9;74KNMGAE1h<6+Z<6MqcJ36UP+JAi701 � �!* .$# � . 7 #� .$#$. 2 . +��-& � . ��+ ! � �"! 2 .)� - & . � *'!(# � � �:7 � -�- !

� ! 7 � &"�$6 ! + � )( 602 $"7 � .$#$. 2 . +�� - � .$# � . !

� � �� . 2�& (#* � & 4(687�+ � # + � �� # � 2 . +��,+ ( +,6 .��( +$+ * )� � .$#(. 2 . +�� - � �� . + � (� 7 � - .$# � .

�� $6 ! + � )( 6G2 � #$. 2 . + � � -

+JAE1436K870+^oqF}MG36-.c�B9GOi3E+h7³ÎqF}+s<D>�/J5N/JUP+JAQ7)MGAmF6-0Mq<R36K87C36AE+|UP/J7��EMq<6+fOi36KSLT/J-4Kk�B+h5d9]F6-0Mq<R3EcJ74KNMGA�3674K858KN10/2+F}MG36-Pc2MGAE1474-436K8-0+�5?>�/J5N/JUP+JAi7�+J7g9;F6F658KNOQ3E+�5d9[-0´Jt^5N+�10/JUn9;AQ74KNOi3E+�9;F6F6-0MGF6-4KN/2+¶70MG367P+JA 9;F6F658KNOi3B9;AQ7n5d974-:9;AE1«j�MG-4Un9;74KNMGA~1436-f5N+21hAEMQ+J3E<61h�E5N1xo}1:9;AE1fMG36\658KN+J-Z5d9mtT+21474KNMGA�<6+�5d9mF6K85N+g<6+21sAEMq+J3E<61f74-:9;K870/21x_ IMG36-5N+21�/J5N/JUP+JAi701e<6+P7ÏÎQF}+PAEMGU�\6-0+m+J7�KN<6+JAi74Kk�Bcx9;70+J36-xo�c2+J5d9¶+2107]74-0´21�10K8UgF65N+^o,F636KN10OQ3,> K85W143*)P7�<6+PL^9;583E+J-5?>@9;7474-4K8\6367s+J7)<D>�+JUgF6K85N+J-s5N+fA,+f3E<[9;K8AE14KD74-:9;K870/n�4$6 ( � .�� . � ��( 7&� �$6 ! + � )( 6G2 $"7 �� #$. 2 . + � .(#$. 2 . + �

-!

.(#$. 2 . + �-&�� . � � ��(687�� * � . � � 2 # � � � ��$+ � - �� ( + . � � !�� & 4 * � !"�.(#$. 2 . + � - �

�� $6 ! + � )( 6G2 $"7 � -

4$6 ( � .�� . � ��( 7&� �$6 ! + � )( 6G2 $0+ �� #$. 2 . + � .(#$. 2 . + �-

!

.(#$. 2 . + �-&�� . � � ��(687�� * � . � � 2 # � � � �&� ! � � - �� ( + . � � !�� & 4 * � !"�.(#$. 2 . + � - �

�� $6 ! + � )( 6G2 $0+ � -

�MG36-s5N+21HA,+f3E<61|<6+f7ÏÎQF}+]+YbRF6-0+21014KNMGA,oRK85Dj?9;367HLT/J-4Kk�B+J-)5N+]cx9G1]�4$6 ( � .�� . � ��( 7&� �$6 ! + � )( 6G2 $ . �� #$. 2 . + � .(#$. 2 . + �

-!

� #$. 2 . + � ! � ! 7 # � � 6 . � *'# � � � 6 . � *"# � � �

� #$. 2 . + � � � ��! 7 # �G6 . + �

7 � � ! 7 � & !'! � � ! 7 # � � #(. 2 . +�� "! 2 . �.(#$. 2 . + � � � 4 ##* � � -�� ! 7 � & !"! � � ! 7 # � � #$. 2 . +�� "! 2 .)�.(#$. 2 . + � � �

�( 7 � � - - !� ! 7 # �$6 . + � � ! 7 � & � . � � ! 7 # �G6 . + � #$. 2 . + � �� '! 2 .)�.$#(. 2 . +��

.� - �

� ! 7 � &"�$6 ! + � )( 602 � #$. 2 . + � � � ! 7 # �$6 . + � � � - �� ! 7 � &"�$6 ! + � )( 602 � #$. 2 . + � � � ! 7 # �$6 . + � � � - �6 . � *'# � � � � � #(. 2 . +�� - � ( + . � � !�� & 4 ( 4 � - �


6 . � *'# � � � � � #(. 2 . +�� - � ( + . � � !�� & 4 ( 4 � - �7 #� 6 . � *'# � � & � . � � � �$687�� * � . � � 2 # � - & . � *'!(# � � � �&� ! � � - &(&

6 . � *"# � � & � . � � ��(687�� * � . � � 2 # � - & . � *'!(# � � � �&� ! � � - - !.(#$. 2 . + �-&�� . � � � �$687�� * � . � � 2 # � � � �&� ! � � - � .$# � . !

.(#$. 2 . + �-&�� . � � � �$687�� * � . � � 2 # � � � ��$+ � - � �� . +)� (� 7 #� - .(# � .� ( + . � � !�� & 4 * � ! � .$#(. 2 . +�� - � .$# � . 7 #� � ! 7 � & !'! � � ! 7 # � � #(. 2 . +�� "! 2 . �.(#$. 2 . + � � � + � -�- !� ! 7 # �$6 . + � � ! 7 � & � . � � ! 7 # �G6 . + � #$. 2 . + � �� '! 2 .)�.$#(. 2 . +�� + � - �� ! 7 � &"�$6 ! + � )( 602 � #$. 2 . + � � � ! 7 # �$6 . + � � � - �6 . � *'# � � � � � #(. 2 . +�� - � ( + . � � !�� & 4 ( 4 � - �.$#(. 2 . +�� &�� . � � ��$6 7 � * � .)� �>2 # � � 6 . � *'# � � & � . � � � �$687�� * � . � � 2 # � - - �� ( + . � � !�� & 4 * � ! � .$#(. 2 . +�� - � .$# � . !

� ! 7 # �$6 . + � � ! 7 � & � . � � ! 7 # �G6 . + � #$. 2 . + � �� '! 2 .)�.$#(. 2 . +�� :7 � - �� ! 7 � &"�$6 ! + � )( 602 � #$. 2 . + � � � ! 7 # �$6 . + � � � - �6 . � *'# � � � � � #(. 2 . +�� - � ( + . � � !�� & 4 ( 4 � - �.$#(. 2 . +�� &�� . � � ��$6 7 � * � .)� �>2 # � � 6 . � *'# � � & � . � � � �$687�� * � . � � 2 # � - - �� ( + . � � !�� & 4 * � ! � .$#(. 2 . +�� - � �� . + � (� 7 � - .$# � .

�� $6 ! + � )( 6G2 $ . � -

*�9�� <6+e5d9mt^-:9;UgUn9;K8-0+n9;\E1474-:9;K870+g+2107f/J70+JAE<R3E+eF}MG36-Z70+JA6K8-Zc2MGUgF670+P<6+ec2+J7a9;7474-4K8\6367]1436-f5N+21/J5N/JUP+JAi701�� / 2 # �". 6 �57 ( +(�� & � � . + ��( �87�+ �(� � 1 � � � � � F � � � � � �� + 1 + � � ! ��-& 2 # � 2 # � �� ! � � � �$+ - � � �(+ � � �� + .��(�. � 4 ##* � � . -�� . � �( 7 � � . -�� + � 7 - �� +�+ 1 � + . � ! � �-& 2 #�� + + � � � � �� + � - �� +�+ 1 � + + � ! � �-& 2 #�� + 7 � � � � �� + � - �� +�+ 1 � + 7 � ! � �-& 2 #�� + 4 #�* � �� +�� + )( 7 � �� +��

;�AR�EA,oB1436-H36A�F6-0MGt^-:9;UgUP+�9;\E1474-:9;K87|<6/Y�EA6K,FB9;-|5N+]<6MQcJ36UP+JAQ7 � �[*�1436K8LG9;AQ7a�� / 2 # �". 6 �57 ( +(�� & � � . + ��( �87�+ �(��01 � � � � � F � � � � � �� +�� . � � � + ��

!� ��$6 ! 7�� . �92 # &"� �)��

� . �� . �� . � � + �GE �� + � �� . �� )( 7 � � �� . � � + � D �� + � �� . �

�� -:9;AE1«jlMG-4Un9;74KNMGAE1h<6+Z<6MqcJ36UP+JAi701 � �!*�� . �� 4 #�* � � �� . �� . � � 7�� / �� 7�� . �� )( 7 � � �� . �� . � � 7�� 7�� . �� 4 ##* � � �� . � � + � � �� + � �� . �� . �

�� . �� . �

MGA¶MG\674KN+JAQ7)5N+Z-0/21436587:9;7a�� / 2 # �". 6 �57 ( +(�� & � � . + ��( �87�+ �(�� + �� . 2 # �� $+ � �� . 2 # �� &� ! � � �� . 2 # � � �&� ! � � � � + 2 # � � �&� ! � � �GE �� + � �� . �� )( 7 �� )( 7 �� . 2 # � � �&� ! � � � � + 2 # � � �&� ! � � � D �� + � �� . �

�� . �� 4 #�* �� 4 #�* �� . 2 # �� $+ � �� . 2 # � � ��$+ � � � 7 2 # � � � �(+ � � / �� 7�� . �� )( 7 �� )( 7 �� . 2 # � � ��$+ � �� . 2 # � � � �(+ � � � 7 2 # �� $+ � �� 7�� . �� 4 ##* �� 4 ##* �� . 2 # � � �� ! � � � � + 2 # � � �� ! � � � � �� + � �� . �

�� . �� . �

�� . �

MG{¶MGA�F}+J367)c2MGAE147:9;70+J-hOi3E+f70MG3670+21|5N+21)+YbqF6-0+21:14KNMGAE1)AE+]c2MGAQ70+JAB9;Ai7fOi3E+Z<6+21|AEMGUa\6-0+21s10MGAi7|<6/210K8t^AE/2+21c2MGUgUP+e147:9;74KNOQ3E+21s+J7h5N+21h9;3674-0+21fc2MGUgUP+e<RÎqAB9;UgKNOi3E+21x_S¬sAE+]74-:9;AE1«j�MG-4Un9;74KNMGA�+YbR/2cJ367:9;AQ7h5N+21f+YbRF6-0+21«X14KNMGAE1)107:9;74KNOi3E+21HF}+J367s9;5NMG-01)VJ74-0+�9;F6F658KNOi3E/2+ZF}MG36-|MGF674K8UgKN10+J-|5N+fF6-0MGt^-:9;UgUP+^_2

�sAg-0+J74KN+JAE<R-:9Z<6+C5?>�+YbR+JUgF65N+)F6-0/2c2/2<6+JAi7`5?>@9;F6F6-0Mqc��E+)tT/JAE/J-:9;5N+)F}MG36-I5d9fc2MGAE1074-43EcJ74KNMGAm<6+21�UP/J7��EMq<6+21<6+Z74-:9;AE1«j�MG-4Un9;74KNMGA�F}MG36-|c��B9GOQ3E+Z7ÏÎQF}+Z<D>�/J5N/JUP+JAi7e�� 9;K8t^36K8585N+J-)5d9e74-:9;AE1«j�MG-4Un9;74KNMGA[+JA�j�MGAEcJ74KNMGA¶<6+21C�E5N1|<6+Z5?>�/J5N/JUP+JAi7fpe74-:9;AE1«j�MG-4UP+J-xo� 9;F6F658KNOi3E+J-|-0/2cJ36-014K8LT+JUP+JAi7h5d9�74-:9;AE1«j�MG-4Un9;74KNMGA[1436-H5N+21)/J5N/JUP/JAQ701)�E5N1yo� K8Ai70+J-0cx9;5N+J-s5N+21|9GcJ74KNMGAE1|10/JUn9;AQ74KNOi3E+21|FSMG36-|5?>�/JLG9;583B9;74KNMGA¶<6+21h9;7474-4K8\636701xoE+J7� <6/JF6K85N+J-=5N+21=/J5N/JUP+JAQ701=�E5N1W<6+C5d9fF6K85N+)<6+21=/J5N/JUP+JAQ701`74-:9;K870/21`FSMG36-=+JUgF6K85N+J-W5?>�/J5N/JUP+JAi7`F}´J-0+H5NMG-010OQ3E+5N+Z<6+J-4A6KN+J-)�E5N1|9e/J70/]74-:9;K870/]+J7)Oi3E+]5N+21|9;7474-4K8\636701|<6+f5?>�/J5N/JUP+JAQ7sF}´J-0+ZMGAi7|/J70/acx9;5NcJ365N/21x_*=>�+YbR+JUgF65N+�<6+m5?>@9;AB9;58ÎR10+�<6+21�UPMGUP+JAQ701P<6+m58Kd9;KN10MGA Oi3E+mAEMG3E1eLT+JAEMGAE1e<6+mF6-0/21:+JAi70+J-gK858583E1474-0+�36Acx9;5NcJ365=<D>@9;7474-4K8\6367]F6-0MGt^-0+21010KkjC1436-f5?>@9;-4\6-0+P<R3�<6MqcJ36UP+JAi7 � �!*=_�I9;-]c2MGAQ74-0+^o,5?>@9;7474-4K8\6367ZUPMGUP+JAQ7�<6+


58Kd9;KN10MGA�+2147Z14ÎqAi7��E/J74KN10/^_DÍÏ5�+2147Z<6MGAEceFSM^1010K8\65N+�<6+�5N+ecx9;5NcJ365N+J-a1:9;AE1Z9Gc2c2/2<6+J-Z5d9mF6K85N+g10MG3E1h5N+e10MGUgUP+J7x_?.MGAE14KN<6/J-0MGAE1CUn9;K8AQ70+JAB9;Ai7H5?>�+Yb6+JUgF65N+h<R3�7³ÎqFB9;tT+f<6/ �4p�9;\}MG-0<6/h9;3�c��B9;F6K874-0+hF6-0/2c2/2<6+JAi7HF}MG36-.K858583E1474-0+J-5?>@9Gc2c2´21sp�5d9gF6K85N+fFSMG36-)-0+JUgF65d9Gc2+J-s36A¶9Gc2c2´21sp�36A[9;7474-4K8\6367 �E/J-4K870/]MG\670+JAi3[FB9;-|14K8UgF65N+Z-0+2c2MGF6KN+^_ �� £Q¥�� w£A� *�9[� ��c2MG-4-0+214F}MGAE<E9;Ai7Pp�5d9¶t^-:9;UgUn9;K8-0+�9;7474-4K8\63E/2+�<6+n5?>�+Yb6+JUgF65N+ �q_ � 1x>�/JAEMGAEc2+c2MGUgUP+]1436K87�� / 2 # �". 6 �57 ( +(�� & � � . + ��( �87�+ �(� � 1 � � � � � F � � � � � �� + 1 + � � ! ��-&"��(4 . � ��(4 .�� 6 .$.(# � . +�� 7 . 6 - � 1 �� 1 � � �� + � � + � - �� +�+ 1 � + � � ! � �-&"��$4 .�� + + � � � � �� + � - �� +�+ 1 � + + � ! � �-&"��$4 .�� + � 7 � � � � � ��1 -�- �� +�+ 1 � + � ! � �-& 2 #�� + 1 � � � � �� + � - �� +�+ 1 � + 1 � ! � �-& 2 #��. +��(6 .(. � �� + � �� 1 � � � �� + 6 .(.$# �� +�� + . + �87 . 6 �� +�� + � � �� + � �

�58367��G7]OQ3E+e<D> 3674K858KN10+J-Z36AE+�7:9;\65N+g<6+21sÎqUa\}MG5N+21ZF}MG36-fUP/JUPMG-4KN10+J-Z5N+�7³ÎqFS+e<6+21hKN<6+JAi74Kk�Bcx9;70+J36-01xo�AEMG3E19±�4MG3670MGAE1C36A�9;7474-4K8\6367H7ÏÎQF}+Z9;3Rb�/J5N/JUP+JAQ701HKN<6+JAi74Kk�Bcx9;70+J36-|OQ36K}LG9�VJ74-0+hLG9;583E/hFB9;-C5d9�74-:9;AE1«j�MG-4Un9;74KNMGA,_?.MGAE14KN<6/J-0MGAE1|5d9eF"�6-:9G10+g> 6 .(.$# 7�� 7�� 7�� D >610MG3E1)5d9�jlMG-4UP+Z<D> 36A[<6MQcJ36UP+JAQ7 � �[* �� / 2 # �". 6 �57 ( +(�� & � � . + ��( �87�+ �(��01 � � � � � F � � � � � �� +�� + �� (4 . � &"�� + � � 6 .$.$# � � �� + �� 1 . +��$6 .$. �� "7�� 1��

�� 1 . +��(6 .$. �� "7�� 1��

�� 1 . +��(6 .(. �� D � �'7�� D �� 1��

��

*�9 74-:9;AE1«j�MG-4Un9;74KNMGA�MG\670+JAQ3E+ p FB9;-474K8-�<6+21¶-0´Jt^5N+21�10/JUn9;AQ74KNOi3E+21�<6+�5d9 t^-:9;UgUn9;K8-0+ 9;7474-4K8\63E/2+ 10+c2MGAE1474-436K87`c2MGUgUP+)5d9hF6-0/2c2/2<6+JAi70+)74-:9;AE14jlMG-4Un9;74KNMGA,_Q��>@9;\}MG-0<Do^MGAP/2cJ-4K87=5d9hUP/J7��EMq<6+)<D>@9;K8t^36K8585d9;tT+|c�B9;-«XtT/2+]<D>@9;F6F}+J5N+J-)5N+21HUP/J7��EMq<6+]<6+Z74-:9;AE1«j�MG-4Un9;74KNMGAE1|c2MG-4-0+210FSMGAE<E9;AQ7hpgc�B9GcJ36A¶<6+21)7ÏÎQF}+21)<D>�/J5N+JUP+JAi701��4$6 ( � .�� . � ��( 7&� �$6 ! + � )( 6G2 � #$. 2 . + � �

�� -:9;AE1«jlMG-4Un9;74KNMGAE1h<6+Z<6MqcJ36UP+JAi701 � �!*� #$. 2 . + � .(#$. 2 . + �-

!

7 � .$#$. 2 . +��-& � . ��+ ! � �"! 2 .)� - & . � *'!(# � � � � � -�- !� ! 7 � &"�$6 ! + � )( 602 $ � � .$#$. 2 . +�� - � .$# � . 7 #� .$#$. 2 . +��-& � . ��+ ! � �"! 2 .)� - & . � *'!(# � � � + � -�- !� ! 7 � &"�$6 ! + � )( 602 $�+ � .$#$. 2 . +�� - � .$# � . 7 #� .$#$. 2 . +��-& � . ��+ ! � �"! 2 .)� - & . � *'!(# � � � � -�- !� ! 7 � &"�$6 ! + � )( 602 $ � .$#$. 2 . +�� - � .$# � . 7 #� .$#$. 2 . +��-& � . ��+ ! � �"! 2 .)� - & . � *'!(# � � �:1 � -�- !� ! 7 � &"�$6 ! + � )( 602 $"1 � .$#$. 2 . +�� - � .$# � . !

� � �� . 2�& (#* � & 4(687�+ � # + � �� # � 2 . +��,+ ( +,6 .��( +$+ * )� � .$#(. 2 . +�� - � �� . + � (� 7 � - .$# � .

�� $6 ! + � )( 6G2 � #$. 2 . + � � -

*�9CUP/J7��EMq<6+`<6+=74-:9;AE1«jlMG-4Un9;74KNMGA�<6+21�/J5N/JUP+JAQ701�<6+�7ÏÎQF}+ �Z9;F6F658KNOi3E+`-0/2cJ36-014K8LT+JUP+JAi7I5d9.74-:9;AE1«j�MG-4Un9;74KNMGA1436-)10+21|<6+J3Rb�/J5N/JUP+JAQ701)�E5N1)<6+]7³ÎqFS+ + +J7 �4$6 ( � .�� . � ��( 7&� �$6 ! + � )( 6G2 $ � �� #$. 2 . + � .(#$. 2 . + �

-!

� #$. 2 . + � ! � ! 7 # � � 6 . � *'# � � � 6 . � *"# � � �

� #$. 2 . + � � � ��! 7 # �G6 . + �

��! 7 # �G6 . +�� ! 7 � & � . � � ! 7 # �$6 . + � #(. 2 . +�� '! 2 . � .$#$. 2 . +�� + � - �� ! 7 � &$�(6 ! + � �( 602 � #(. 2 . +�� ! 7 # �G6 . + � � � - ��! 7 # �G6 . +�� ! 7 � & � . � � ! 7 # �$6 . + � #(. 2 . +�� '! 2 . � .$#$. 2 . +�� - �� ! 7 � &$�(6 ! + � �( 602 � #(. 2 . +�� ! 7 # �G6 . + � � � - �6 . � *"# � � � � � #$. 2 . +�� - � ( + . � � !�� & 4 ( 4 � - �6 . � *"# � � � � � #$. 2 . +�� - � ( + . � � !�� & 4 ( 4 � - �� ( + . � � !�� & 4 * � !"�.(#$. 2 . + � - �

�� (6 ! + � �( 602 $ �"� -

*�9�74-:9;AE1«j�MG-4Un9;74KNMGA¶1436- + +2147H14K8UgK85d9;K8-0+a9;3Rbm74-:9;AE14jlMG-4Un9;74KNMGAE1s<6+f5?>�+YbR+JUgF65N+ZF6-0/2c2/2<6+JAQ7)F636KN10OQ3E+Z1436-5N+21|/J5N/JUP+JAQ701 + oR5?>@9;7474-4K8\6367|7ÏÎQF}+]+2147|10ÎQAQ7��E/J74KN10/^_EÍÏ5�143*)P7|<6MGAEc]<6+]LG9;583E+J-)5?>@9;7474-4K8\6367h+JA�j�MGAEcJ74KNMGA[<R37³ÎqF}+Z<6+Z5?>�/J5N/JUP+JAi7|�E5N1auw-0/2+J5�MG3¶+JAQ74KN+J-�zZ�4$6 ( � .�� . � ��( 7&� �$6 ! + � )( 6G2 $�+ �� #$. 2 . + � .(#$. 2 . + �-!

� #$. 2 . + � ! � ! 7 # � � 6 . � *'# � � � 6 . � *"# � � �

� #$. 2 . + � � � ��! 7 # �G6 . + �


7 � � ! 7 � & !'! � � ! 7 # � � #(. 2 . +�� "! 2 . �.(#$. 2 . + � � � 6 .$.$# � - - !.$#(. 2 . +�� &�� . � � ��$6 7 � * � .)� � ��$4 . � � �96 .$.(# � - �� ( + . � � !�� & 4 * � ! � .$#(. 2 . +�� - � .$# � . !

.$#(. 2 . +�� &�� . � � ��$6 7 � * � .)� � ��$4 . � � �. +�� 7 . 6 � - �

� ( + . � � !�� & 4 * � ! � .$#(. 2 . +�� - � �� . + � (� 7 � - .$# � . �� $6 ! + � )( 6G2 $�+ � -

*�9eUP/J7��EMq<6+]<6+f74-:9;AE1«j�MG-4Un9;74KNMGA[<6+21|/J5N/JUP+JAi701h<6+Z7³ÎqFS+ c2MGAEc2+JAi74-0+a5N+21HAEMG74KNMGAE1)K8UgF}MG-47:9;Ai70+21sKNcJK`�4$6 ( � .�� . � ��( 7&� �$6 ! + � )( 6G2 $ �� #$. 2 . + � .(#$. 2 . + �

-!

� #$. 2 . + � ! � ! 7 # � � 6 . � *'# � � � 6 . � *"# � � �

� #$. 2 . + � � � ��! 7 # �G6 . + �

7 � � ! 7 � & !'! � � ! 7 # � � #(. 2 . +�� "! 2 . �.(#$. 2 . + � � �� - - !

� ! 7 # �$6 . + � � ! 7 � & � . � � ! 7 # �G6 . + � #$. 2 . + � �� '! 2 .)�.$#(. 2 . +�� - �� ! 7 � &"�$6 ! + � )( 602 � #$. 2 . + � � � ! 7 # �$6 . + � � � - �� ! 7 # �$6 . + � � ! 7 � & � . � � ! 7 # �G6 . + � #$. 2 . + � �� '! 2 .)�.$#(. 2 . +�� :1 � - �� ! 7 � &"�$6 ! + � )( 602 � #$. 2 . + � � � ! 7 # �$6 . + � � � - ��(� � #$. 2 . +�� - � ( + . � � !�� & 4 .(. � � -�- &�� . � � ��$6 7 � * � .)�

� ��(4 . � �� #$. 2 . + � - � ( + . � � !�� & 4 .$. �� -�- & � . � � � �$6 7 � * � .)� � � �$4 . � - - �

6 . � *'# � � � � � #(. 2 . +�� - � ( + . � � !�� & 4 ( 4 � - �6 . � *'# � � � � � #(. 2 . +�� - � ( + . � � !�� & 4 ( 4 � - �� ( + . � � !�� & 4 * � ! � .$#(. 2 . +�� - � .$# � . !

� ! 7 # �$6 . + � � ! 7 � & � . � � ! 7 # �G6 . + � #$. 2 . + � �� '! 2 .)�.$#(. 2 . +�� :1 � - �� ! 7 � &"�$6 ! + � )( 602 � #$. 2 . + � � � ! 7 # �$6 . + � � � - ��(� � #$. 2 . +�� - � ( + . � � !�� & 4 .(. � � -�- &�� . � � ��$6 7 � * � .)�

� ��(4 . � �� #$. 2 . + � - � ( + . � � !�� & 4 .$. �� -�- & � . � � � �$6 7 � * � .)� � � �$4 . � - - �

6 . � *'# � � � � � #(. 2 . +�� - � ( + . � � !�� & 4 ( 4 � - �� ( + . � � !�� & 4 * � ! � .$#(. 2 . +�� - � �� . + � (� 7 � - .$# � .

�� $6 ! + � )( 6G2 $ � -

*,MG-010OQ3E+�5d9CF6-0Mq<R3EcJ74KNMGAa3674K858KN1:/2+`+2147L→ I

9;5NMG-01xo25d9HLG9;5N+J36-�<R3�7³ÎqFS+=p|9;7474-4K8\63E+J-IpC5?> KN<6+JAQ74Kk�Bcx9;70+J36-�+2107c2+J5836KB<6+|5?>�/J5N/JUP+JAi7W<6+)7³ÎqFS+ + OQ36KB10+C74-0MG36LT+)K8UgUP/2<RKd9;70+JUP+JAQ7H10MG3E1�5N+)10MGUgUP+J7.<6+H5d9fF6K85N+��«3E1470+|9xLG9;AQ7<6+�<6/JF6K85N+J-h5?>�/J5N/JUP+JAQ7 1 FSMG36-f+JUgF6K85N+J-f5?>�/J5N/JUP+JAi7 _S*,MG-010OQ3E+�5d9PF6-0Mq<R3EcJ74KNMGA�3674K858KN10/2+�+2147 L → L � I o9;5NMG-01g5d9!L^9;5N+J36-n<R3 7³ÎqF}+�p�9;7474-4K8\63E+J-mp!5?> KN<6+JAi74Kk�Bcx9;70+J36-�+2147Pc2+J5836K)<R3 <6+J3RbRKN´JUP+�/J5N/JUP+JAi7m10MG3E1g5N+10MGUgUP+J7H<6+h5d9]F6K85N+^oR<6+h7³ÎqF}+ + ox�«3E1470+f92L^9;Ai7)<6+h<6/JF6K85N+J-H5N+21C/J5N/JUP+JAi701 1 +J7 F}MG36-.+JUgF6K85N+J-H5?>�/J5N/JUP+JAQ7 FB9;-0+JAi7x_R*,+21W3674K858KN1:9;74KNMGAE1C<6+ 4 .$. �g+J7 4 .$. �� K858583E1074-0+JAi7C5N+21W9Gc2c2´21HpZ5d9]F6K85N+sc2MGUgUP+sAEMG3E1W5N+21.9xLTMGAE1

�� -:9;AE1«jlMG-4Un9;74KNMGAE1h<6+Z<6MqcJ36UP+JAi701 � �!*Lq3 9;3 c��B9;F6K874-0+[F6-0/2c2/2<6+JAi7�uw5N/JtT´J-0+JUP+JAi7�UPMQ<RKk�B/21nKNcJK|cx9;-PAEMG3E1m9xLTMGAE1nc�EMGKN14Ks<6+�AE+�FB9G1m+JUgF6K85N+J-5?>�/J5N/JUP+JAi7.<6+C7³ÎqFS+��

�oGK8AQ3674K85N+)<E9;AE1=c2+Hc2MGAi70+YbR70+yzY_$(hMG3E1=9;36-4KNMGAE1=F63gUPMq<RKk�B+J-=5N+21=c�EM^10+21=+JAP<6/JF6K85d9;AQ75N+21)/J5N/JUP+JAQ701)�E5N1)c2MG36-:9;AQ701h9xLG9;AQ7|<D>�/JL^9;583E+J-)5d9e-0´Jt^5N+]10/JUn9;AQ74KNOi3E+^_

;�AR�EA,oQ<E9;AE1Wc2+)c2MGAi70+YbR70+^oQ5d9Z74-:9;AE1«j�MG-4Un9;74KNMGAm<6+21W/J5N/JUP+JAi701C<6+)7ÏÎQF}+ 1 c2MGAE14KN1470+|10K8UgF65N+JUP+JAi7Hpf5N+21+JUgF6K85N+J-a�4$6 ( � .�� . � ��( 7&� �$6 ! + � )( 6G2 $"1 �� #$. 2 . + � .(#$. 2 . + �

-!

� ( + . � � !�� & 4 * � !"�.(#$. 2 . + � - � �� $6 ! + � )( 6G2 $"1 � -

*=>@9;F6F658KNcx9;74KNMGA�<6+f5d9e74-:9;AE1«j�MG-4Un9;74KNMGA¶1436-)5?>�+Yb6+JUgF65N+ZF6-0/2c2/2<6+JAQ7|-0+J70MG36-4AE+]5N+Z<6MqcJ36UP+JAi7h1436K8L^9;Ai7a�� / 2 # �". 6 �57 ( +(�� & � � . + ��( �87�+ �(�� + �� + ��(4 . � � 6 .$.$# � � � 6 .(.$# � � �� + �� 1 . +��$6 .$. �� $4 . ��96 .(.$# � �'7&� � �� 1��

�� 1 . +��(6 .$. �� $4 . � � 6 .(.$# � �'7&� � �� 1��

�� 1 . +��(6 .(. �� D � ��(4 . �� 6 .$.(# � �"7�� D �� 1��

��

2

� ��#$��(��

� � ¬ �� _ � �EM6o<%a_ � +J7��6K?o`+J7��E_`¬s5858Un9;A,_�#'3^� 4S�v�8�^�³�Y�q®:�� .®Y�v� �J� 4E��a�³� �JÑi�E��J�6�Y��J� 3G�q�l�w��Y_ÍÏAi70+J-`<RK874KNMGAE1xo � �0�� _ � -4K � � � �B_ � -4KN+2<R5?_��!�G�Y�³�Y®Y�v�q� )�?G�Q�8�G®�� 54�®0�� 3G�6�Y_ ��> %|+JK85858ÎTo � �� R_ !h¬ � � � �B_ !hMGFScJ-0M;jl7W+J7 �E_Q¬s5858Un9;A,_ � �B�l® 3 � ��2�l� 3G�¶��3 � �R��3G�P�^�?� ��ÑR� 3^®�� ,�G�Q^�R�xQ��Z�^� � #'3G� 4��qÐ�?�T�l� 3G��_ � <6<RKN10MGARX �~+2145N+JÎTo � � � � _ �[KNc � � � � _ �[KNc��B9;-0<D_ � �� k�G�qT�xi�e�J�C�54�4�� 0�^�l� 3G�6�Y_ ;�ÎQ-0MG585N+21yo � �� ^_ I+J-:9 � I+J-45N<6Mqc^_�c2MGU�_ 46�Y®Y� �Y�G�� |�Y®��i��G�B�?� �T_ ! ��$4 ) �� & 4 . 6 # � (�� & �#( 2 � 4 . 6 # F@& � � 4 ( � � 4 . 6 # ��(+-& ! �02 #6_ I+J-4\� I+J-45N<6Mqc^_�c2MGU�_ 4S®4�Y� ®0� � �)�J®�� ®4�?G�Q�8�G® � �24�®4�Y�:�� 3G�6�J_

! ��(4 ) �� & 4 . 6 # � (�� & �#( 2 � 4 . 6 # F<& � � 4 ( � � 4 . 6 # 6 . & ! �02 #E_ �Îq7 � � K870+]K8Ai70+J-4AE+J7|FQÎQ7��EMGA,_ ! ��(4 ) �� & 4�� !%( +-& ( 6 � � _ � 7:9 �� _ � _ � 7:9;AE<RKN1��,_ ��^�?� %S�l®��2�l�q®4�� $3G®��l�wÑi��g�G� � %�3 'Y��`�^®4� �C®��w� �J� 4��N��Y_ � <6<RKN10MGARX

�~+2105N+JÎTo � �� _

users.polytech.unice.frusers.polytech.unice.fr/~pfz/COMPILATION/COURS/coursMALENFANT.pdf ·...

Documents

Transcript of users.polytech.unice.frusers.polytech.unice.fr/~pfz/COMPILATION/COURS/coursMALENFANT.pdf ·...